GATE Overflow - Recent questions tagged probability
https://gateoverflow.in/tag/probability
Powered by Question2AnswerMade easy
https://gateoverflow.in/160388/made-easy
<p><img alt="" src="https://gateoverflow.in/?qa=blob&qa_blobid=3453992012750236024"></p>
<p> </p>
<p> </p>
<p>Please tell me how the odd function is getting a positive value over -1/2 to 1/2?</p>Mathematical Logichttps://gateoverflow.in/160388/made-easySun, 15 Oct 2017 17:59:11 +0000PROBABILITY
https://gateoverflow.in/157774/probability
A box containing 4 red balls and 6 black balls . Three balls are selected randomly from the box one after the another, without replacement . The probality that the selected set has one red ball and two black balls is .<br />
<br />
I am getting this (4/10)*(6/9)*(5/8) is it correct And is order have any significance here.?Probabilityhttps://gateoverflow.in/157774/probabilityFri, 06 Oct 2017 06:39:17 +0000BINOMIAL DISTRIBUTION
https://gateoverflow.in/157752/binomial-distribution
Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is----<br />
<br />
I am getting 0.75 can anyone confirm this ?Probabilityhttps://gateoverflow.in/157752/binomial-distributionFri, 06 Oct 2017 05:33:23 +0000Sheldon Ross chapter 4 Random variables Qno-72
https://gateoverflow.in/156385/sheldon-ross-chapter-4-random-variables-qno-72
Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner .Suppose that one of the team is stronger than the other and wins each game with prob 0.6,independently of the outcomes of other games.Find the prob for i=4,5,6,7,,,that the sronger team wins the series in exactly i games.Compare the prob that the stronger team wins with the prob that it would win a 2-out-3 series.Probabilityhttps://gateoverflow.in/156385/sheldon-ross-chapter-4-random-variables-qno-72Sat, 30 Sep 2017 15:46:57 +0000Probability
https://gateoverflow.in/155820/probability
Imagine you are given a bag of n balls. You are told that at least 10% of the balls are blue, and no more than 90% of the balls are red. Asymptotically (for large n) how many balls do you have to draw from the bag to see a blue ball with probability at least 2/3? (You can assume that the balls are drawn with replacement.)Probabilityhttps://gateoverflow.in/155820/probabilityThu, 28 Sep 2017 10:29:26 +0000Probability
https://gateoverflow.in/155533/probability
A train and a bus arrive at random between 9 am and 10 am. The train stops for 10 minutes whereas the bus stops for 'x' minutes. Find 'x' such that the probability that the bus and train meet is 0.5.<br />
<br />
How to approach such type of questions ?Probabilityhttps://gateoverflow.in/155533/probabilityWed, 27 Sep 2017 06:05:08 +0000Probability
https://gateoverflow.in/155136/probability
Let X and Y be independent random variables each taking the values -1 or 1 with probability 1/2. Let Z=XY . Show that X,Y,Z are pairwise independent .<br />
<br />
Are they indepenedent ?Probabilityhttps://gateoverflow.in/155136/probabilityMon, 25 Sep 2017 18:30:19 +0000Sheldon Ross chapter#3 Qno-45
https://gateoverflow.in/153765/sheldon-ross-chapter%233-qno-45
<p>A set of k coupons, each of which is independently a type j coupon with probability
<br>
p<sub>j</sub><sub> </sub>, from j=1 to n ∑ p<sub>j </sub>= 1, is collected. Find the probability that the set contains either
<br>
a type i or a type j coupon.</p>Probabilityhttps://gateoverflow.in/153765/sheldon-ross-chapter%233-qno-45Wed, 20 Sep 2017 17:38:27 +0000Sheldon ross chapter#3 Qno -30
https://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30
Two balls, each equally likely to be colored either red or blue, are put in an urn.<br />
At each stage one of the balls is randomly chosen, its color is noted, and it is<br />
then returned to the urn. If the first two balls chosen are colored red, what is the<br />
probability that<br />
(a) both balls in the urn are colored red;<br />
(b) the next ball chosen will be red?Probabilityhttps://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30Tue, 19 Sep 2017 11:01:23 +0000sheldon M ross 4 ed - chapter-3 qno- 25
https://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25
Fifty-two percent of the students at a certain college are females. Five percent<br />
of the students in this college are majoring in computer science. Two percent of<br />
the students are women majoring in computer science. If a student is selected at<br />
random, find the conditional probability that<br />
(a) this student is female, given that the student is majoring in computer science;<br />
(b) this student is majoring in computer science, given that the student is<br />
female.<br />
<br />
How to solve this qn by growing tree method?Probabilityhttps://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25Mon, 18 Sep 2017 09:01:47 +0000Probability
https://gateoverflow.in/151046/probability
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?<br />
<br />
Ans is 1/3.<br />
<br />
Why this answer does not come when we apply conditional probability?Mathematical Logichttps://gateoverflow.in/151046/probabilitySat, 09 Sep 2017 17:34:48 +0000Probability
https://gateoverflow.in/148385/probability
In the card game bridge, the 52 cards are dealt out equally to 4 players—called East,<br />
West, North, and South. If North and South have a total of 8 spades among them,<br />
what is the probability that East has 3 of the remaining 5 spades?Probabilityhttps://gateoverflow.in/148385/probabilityWed, 30 Aug 2017 03:56:33 +0000probability
https://gateoverflow.in/144372/probability
<p><img alt="" height="201" src="http://gateoverflow.in/?qa=blob&qa_blobid=3799245635594239058" width="652"></p>Probabilityhttps://gateoverflow.in/144372/probabilityTue, 15 Aug 2017 13:28:46 +0000Probability Gate EE 2016
https://gateoverflow.in/143924/probability-gate-ee-2016
Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is _________.Probabilityhttps://gateoverflow.in/143924/probability-gate-ee-2016Sun, 13 Aug 2017 18:59:07 +0000probability
https://gateoverflow.in/142502/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5164991502263664022"></p>Mathematical Logichttps://gateoverflow.in/142502/probabilityTue, 08 Aug 2017 14:49:42 +0000Probability
https://gateoverflow.in/142244/probability
Suppose that in the production of 60-ohm radio<br />
resistors, nondefective items are those that have a<br />
resistance between 58 and 62 ohms and the probability<br />
of a resistor’s being defective is 0.1%.The resistors<br />
are sold in lots of 200, with the guarantee that all<br />
resistors are nondefective. What is the probability that<br />
a given lot will violate this guarantee? (Use the Poisson<br />
distribution.)<br />
<br />
Using bernoulli:18%Engineering Mathematicshttps://gateoverflow.in/142244/probabilityMon, 07 Aug 2017 06:59:26 +0000Sheldon Ross - Probability (2nd chapter)
https://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapter
<p>Poker dice is played by simultaneously rolling 5 dice.Show that</p>
<p>(a) P{no two alike} = .0926;
<br>
(b) P{one pair} = .4630;
<br>
(c) P{two pair} = .2315;
<br>
(d) P{three alike} = .1543;
<br>
(e) P{full house} = .0386;
<br>
(f) P{four alike} = .0193;
<br>
(g) P{five alike} = .0008.</p>
<p><span class="marker">My doubt is how is this different from poker played by cards? Is it that when we play via dice the order of the dice outcome matters which doesn't in case of cards.(i.e the order of cards in hand). So if we think the case of having one pair as </span></p>
<p><span class="marker"><6 6 5 1 2> and <6 5 1 2 6> both outcomes are different?</span></p>
<p><span class="marker">but <6(1st six) 5 1 2 6 (second six)> and <6(2nd six) 5 1 2 6(1st six)> both are same,since its the same one pair but the pairs doesn't generate new outcome when position is changed.</span></p>
<p>i.e for question (b) probability is = 6C1 (for selecting pair outcome) * 5C2 (possibility of selecting a pair of hand out of five,but order does not matter when pair partners are exchanged) * 5 * 4* 3 (because order matters of the outcomes of other non-pairs) this total divided by 6^5. Is my assumption true?</p>Combinatoryhttps://gateoverflow.in/141823/sheldon-ross-probability-2nd-chapterSat, 05 Aug 2017 07:41:33 +0000Probability: Poisson distribution calculation vs normal probability calculation
https://gateoverflow.in/141096/probability-distribution-calculation-probability-calculation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6871126998631182856"></p>
<p>In this question if we do simply probability calculation then it is 8/20 40%</p>
<p>but when I am appling poisson distribution then it is 40.4%.</p>
<p>why we are getting two different answers??</p>Mathematical Logichttps://gateoverflow.in/141096/probability-distribution-calculation-probability-calculationTue, 01 Aug 2017 18:18:46 +0000Conditional Probability
https://gateoverflow.in/141030/conditional-probability
If the occurrence of some events are dependent on the occurrence of an event A then sum of all the joint<br />
<br />
probabilities in which the occurrence of event A is considered gives the<br />
<br />
a) Subjective probability of event A<br />
<br />
b) Classical probability of event A<br />
<br />
c) Conditional probability of event A<br />
<br />
d) Marginal Probability of event A<br />
<br />
e) Relative frequency of occurrence of event AProbabilityhttps://gateoverflow.in/141030/conditional-probabilityTue, 01 Aug 2017 10:45:25 +0000Probability fair and unfair coin together
https://gateoverflow.in/138892/probability-fair-and-unfair-coin-together
<p>How to solve this question.</p>
<p><a rel="nofollow" href="https://www.facebook.com/photo.php?fbid=1131807666919473&set=gm.1597917393573841&type=3&theater">https://www.facebook.com/photo.php?fbid=1131807666919473&set=gm.1597917393573841&type=3&theater</a></p>
<p>A box contains 5 fair coins and 5 biased coins. Each biased coin has a probability of a head 4/5. A coin is drawn at random from the box and tossed. Then a second coin is drawn at random from the box (without replacing the first one.) Given that the first coin has shown head, the conditional probability that the second coin is fair, is </p>
<p>a) 20/39</p>
<p>b) 20/37</p>
<p>c) 1/2</p>
<p>d) 7/13</p>Databaseshttps://gateoverflow.in/138892/probability-fair-and-unfair-coin-togetherThu, 20 Jul 2017 13:43:34 +0000Discreate Random Variable (Rose_8th Edition)
https://gateoverflow.in/138439/discreate-random-variable-rose_8th-edition
Three balls are to be randomly selected without replacement from an urn containing 20 balls numbered 1 through 20. If we bet that at least one of the balls that are drawn has a number as large as or larger than 17, what is the probability that we win the bet?<br />
<br />
My Approach through random variables:<br />
<br />
let X is the random variable defined as:<br />
<br />
X = number of balls having the number on them >= 17 in three drawn.<br />
<br />
In the question, they have asked for at least 1 then we can place the values of X are 1,2,3;<br />
<br />
P(X = 1 ) = (4/20) * (16/19) * (15 / 18) = 0.14035<br />
<br />
P(X = 2 ) = (4/20) * (3/19) * (16 / 18) = 0.02807<br />
<br />
P(X = 3 ) = (4/20) * (3/19) * (2 / 18) = 0.00350<br />
<br />
Prob of wining bet = P(X=1) + P(X=2) + P(X=3) <br />
<br />
= 0.17192<br />
<br />
but the answer is 0.508<br />
<br />
what is wrong with this approach.Combinatoryhttps://gateoverflow.in/138439/discreate-random-variable-rose_8th-editionTue, 18 Jul 2017 05:33:06 +0000Probability # Distribution
https://gateoverflow.in/137764/probability-%23-distribution
A traffic office imposes on an average 5 number of penalities daily on traffic violators.Assume that the number of the penalties on different days is independent and follows a Poisson distribution.The probability that there will be less than 4 penalties in a day is _______________ ?Mathematical Logichttps://gateoverflow.in/137764/probability-%23-distributionFri, 14 Jul 2017 09:22:11 +0000probability
https://gateoverflow.in/137763/probability
a lot consists of 12 good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is?Probabilityhttps://gateoverflow.in/137763/probabilityFri, 14 Jul 2017 09:19:07 +0000probability
https://gateoverflow.in/137762/probability
a lot consists of good pencils, 6 with minor defects and 2 with major defects. A pencil is chosen at random. The probability that this pencil is not defective is?Probabilityhttps://gateoverflow.in/137762/probabilityFri, 14 Jul 2017 09:18:35 +0000Probability
https://gateoverflow.in/137761/probability
A box contains 4 red balls and 6 black balls .Three balls are selected randomly from the box one after another without replacement .The probability that the selected set contains one red ball and two black ball is <br />
<br />
A)1/20<br />
<br />
B) 1/12<br />
<br />
C) 3/10<br />
<br />
D)1/2Mathematical Logichttps://gateoverflow.in/137761/probabilityFri, 14 Jul 2017 09:13:45 +0000Probability
https://gateoverflow.in/137756/probability
A fair (unbiased) coin was tosssed four times in succession and resulted in the following outcomes:<br />
<br />
i)Head , ii) Head, iii) Head iv)Head. The probability of obtaining a "Tail" when a coin is tossed again is<br />
<br />
A) 0<br />
<br />
B) 1/2<br />
<br />
C) 4/5<br />
<br />
D) 1/5Mathematical Logichttps://gateoverflow.in/137756/probabilityFri, 14 Jul 2017 09:08:30 +0000Probability
https://gateoverflow.in/137755/probability
A fair coin is tossed till a head appears for the first time .The probability that the number of required tosses is odd.<br />
<br />
A) 1/3<br />
<br />
B) 1/2<br />
<br />
C)2/3<br />
<br />
D)3/4Mathematical Logichttps://gateoverflow.in/137755/probabilityFri, 14 Jul 2017 09:01:30 +0000# Probability
https://gateoverflow.in/137733/%23-probability
<p><strong>What is the expected no. of heads that come up when fair coin is flipped five times?</strong></p>Mathematical Logichttps://gateoverflow.in/137733/%23-probabilityFri, 14 Jul 2017 07:03:36 +0000probability
https://gateoverflow.in/137217/probability
<p><em>India plays two matches each with West I</em><em>ndies</em><em> and Srilanka. In any </em><em>match</em><em> the probabilities of I</em><em>ndia</em><em> getting points 0,1 and 2 are 0.45,0.05 and 0.50 respectively. Assuming that the outcomes are independent, the probability of I</em><em>ndia</em><em> getting </em><em>at least</em><em> 7 points is?</em></p>
<p><em>a) 0.8750 b) 0.0875 c) 0.0625 d) 0.0250</em></p>Probabilityhttps://gateoverflow.in/137217/probabilityTue, 11 Jul 2017 09:10:49 +0000Probability posion distribtuion
https://gateoverflow.in/135554/probability-posion-distribtuion
the tailors in the stitching shop on an average stitches 3 shorts in an hour,stitching has a poison distribution.During a particular hour ,what is the probability that number of shirts stitched are 5 or more?<br />
<br />
a) .8571<br />
<br />
b.) .8152<br />
<br />
c.) .1848<br />
<br />
d.).1439Probabilityhttps://gateoverflow.in/135554/probability-posion-distribtuionSat, 01 Jul 2017 07:43:11 +0000Gate EE 17
https://gateoverflow.in/135069/gate-ee-17
Assume that in a traffic junction, the cycle of traffic signal lights is 2 minutes of green(vehicle does not stop) and 3 minutes of red (vehicle stops). Consider the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time in minutes for the vehicle at the junction is _________Probabilityhttps://gateoverflow.in/135069/gate-ee-17Wed, 28 Jun 2017 10:26:41 +0000Sheldon Ross Chapter 1 Example 3c
https://gateoverflow.in/134909/sheldon-ross-chapter-1-example-3c
Ms. Jones has 10 books that she is going to put on her bookshelf. Of these, 4 are mathematics books, 3 are chemistry books, 2 are history books, and 1 is a language book. Ms. Jones wants to arrange her books so that all the books dealing with the same subject are together on the shelf. How many different arrangements are possible? <br />
<br />
Please provide a different explanation rather than the textbook one.Combinatoryhttps://gateoverflow.in/134909/sheldon-ross-chapter-1-example-3cTue, 27 Jun 2017 06:52:14 +0000[Gate 2006 EC] Probability
https://gateoverflow.in/134674/gate-2006-ec-probability
<p>Three companies, X, Y and Z supply computers to a university. The percentage of computers supplied by them and the probability of those being defective are tabulated below.</p>
<table border="1" cellpadding="0" cellspacing="0" style="width:100%">
<tbody>
<tr>
<td> Company</td>
<td> % of computers supplied </td>
<td> Probability of being defective</td>
</tr>
<tr>
<td> X</td>
<td> 60%</td>
<td> 0.01</td>
</tr>
<tr>
<td> Y</td>
<td> 30%</td>
<td> 0.02</td>
</tr>
<tr>
<td> Z</td>
<td> 10%</td>
<td> 0.03</td>
</tr>
</tbody>
</table>
<p>Given that a computer is defective, the probability that it was supplied by Y is: [2 marks]
<br>
(A) 0.1
<br>
(B) 0.2
<br>
(C) 0.3
<br>
(D) 0.4</p>
<p>I got the correct answer by applying bayees theorem. But that theorem is applicable where the events are collectively exhaustive and mutual exclusive. These are collectively exhaustive but i don't think that they are mutually exclusive as Supplying of x does not mean that y wont supply.Please clear this doubt.</p>Probabilityhttps://gateoverflow.in/134674/gate-2006-ec-probabilitySun, 25 Jun 2017 06:07:49 +0000Probability
https://gateoverflow.in/134654/probability
P( A union B)=.6<br />
<br />
P( A intersection B)=.25<br />
<br />
Find P(A`) +P(B`) ? <br />
<br />
where P(A`) means probability of A complement.Mathematical Logichttps://gateoverflow.in/134654/probabilitySat, 24 Jun 2017 20:57:59 +0000IISc PhD
https://gateoverflow.in/132635/iisc-phd
A bag contains Red Balls and Black Balls. Two balls are drawn without replacement. The probability that both the balls drawn are red is 1/2. What is the minimum number of Red and Black Balls for which this probability is satisfied?Probabilityhttps://gateoverflow.in/132635/iisc-phdSun, 11 Jun 2017 07:18:42 +0000Sheldon Ross chapter 2 questions 26
https://gateoverflow.in/132384/sheldon-ross-chapter-2-questions-26
The game of craps is played as follows: A player rolls two dice. If the sum of the dice is either a 2, 3, or 12, the player loses; if the sum is either a 7 or an 11, the player wins. If the outcome is anything else, the player continues to roll the dice until she rolls either the initial outcome or a 7. If the 7 comes first, the player loses, whereas if the initial outcome reoccurs before the 7 appears, the player wins. Compute the probability of a player winning at craps. Hint:Let Ei denote the event that the initial outcome is i and the player wins. The desired probability is $\sum_{i=2}^{12}$P(Ei). To compute P(Ei), define the events Ei,n to be the event that the initial sum is i and the player wins on the nth roll. Argue that P(Ei) =$\sum_{n=1}^{infinte}$ P(Ei,n).Probabilityhttps://gateoverflow.in/132384/sheldon-ross-chapter-2-questions-26Fri, 09 Jun 2017 05:26:43 +0000sheldon ross, chapter 2, question 17
https://gateoverflow.in/132359/sheldon-ross-chapter-2-question-17
If 8 rooks are randomly placed on a chessboard, compute the probability that none of the rooks can caputre any of the others. That is compute the probability that no row or file contains more than one rook.Probabilityhttps://gateoverflow.in/132359/sheldon-ross-chapter-2-question-17Fri, 09 Jun 2017 01:32:42 +0000Probability of dice
https://gateoverflow.in/131870/probability-of-dice
If 4 dice tossed together , what is the probability of sum of these dice will be exactly 20? (want to see some shortcut procedure)Probabilityhttps://gateoverflow.in/131870/probability-of-diceSun, 04 Jun 2017 17:00:17 +0000Probability puzzles
https://gateoverflow.in/130530/probability-puzzles
A grasshopper is sitting on a little stone, which we'll call stone zero. Ahead of him, arranged in a line, are stones one, two, three, et cetera, all the way up to nine. <br />
<br />
The grasshopper would like to reach that ninth stone, for reasons unknown. What we do know is that he'll get there by combining little grasshopper jumps, each of which will take our friend forward by either one or two steps. To be clear, this means the grasshopper has exactly two ways to reach stone two: he could take one big jump, or two little ones. <br />
<br />
How many different paths can the grasshopper take to reach his destination?Probabilityhttps://gateoverflow.in/130530/probability-puzzlesTue, 23 May 2017 10:21:01 +0000Probbility puzzles
https://gateoverflow.in/130529/probbility-puzzles
Three men — conveniently named A, B, and C — are fighting a duel with pistols. It's A's turn to shoot. <br />
<br />
The rules of this duel are rather peculiar: the duelists do not all shoot simultaneously, but instead take turns. A fires at B, B fires at C, and C fires at A; the cycle repeats until there is a single survivor. If you hit your target, you'll fire at the next person on your next turn. <br />
<br />
For example, A might shoot and hit B. With B out of the picture, it would be C's turn to shoot — suppose he misses. Now it's A's turn again, and he fires at C; if he hits, the duel is over, with A the sole survivor. <br />
<br />
To bring in a little probability, suppose A and C each hit their targets with probability 0.5, but that B is a better shot, and hits with probability 0.75 — all shots are independent. <br />
<br />
What's the probability that A wins the duel?Probabilityhttps://gateoverflow.in/130529/probbility-puzzlesTue, 23 May 2017 10:08:48 +0000IIITH-PGEE 2017
https://gateoverflow.in/127525/iiith-pgee-2017
Consider 3 card one having both side painted red another having both side printed black and last having one side black and another side red, 3 cards are put in a hat and are mixed properly, now one card in picked and put down on table, its face up color is red what is probability that another side will be black.Probabilityhttps://gateoverflow.in/127525/iiith-pgee-2017Sun, 30 Apr 2017 18:24:00 +0000Probability
https://gateoverflow.in/125997/probability
Suppose that a particular trait (such as eye color or left-handedness) of a person is classified on the basis of one pair of genes, and suppose that d represents a dominant gene and r a recessive gene. Thus, a person with dd genes is pure dominance, one with rr is pure recessive, and one with rd is hybrid. The pure dominance and the hybrid are alike in appearance. Children receive 1 gene from each parent. If, with respect to a particular trait, 2 hybrid parents have a total of 4 children, what is the probability that 3 of the 4 children have the outward appearance of the dominant gene?Probabilityhttps://gateoverflow.in/125997/probabilityMon, 17 Apr 2017 21:32:07 +0000Probability
https://gateoverflow.in/125717/probability
in a game of bridge the entire deck of 52 cards is dealt out to 4 players.What is the probability that <br />
<br />
i)one of the players receive all 13 spades<br />
<br />
ii )each player receives one ace?Probabilityhttps://gateoverflow.in/125717/probabilitySat, 15 Apr 2017 21:04:10 +0000Probability
https://gateoverflow.in/125714/probability
<p><em>A 5-card poker hand is said to be a full house if it consists of 3 cards of the same denomination and 2 other cards of the same denomination (of course, different from the first denomination). Thus, one kind of full house is three of a kind plus a pair. What is the probability that one is dealt a full house?</em></p>Probabilityhttps://gateoverflow.in/125714/probabilitySat, 15 Apr 2017 20:49:57 +0000Probability Exercise
https://gateoverflow.in/123094/probability-exercise
The chess club of two school consists of 8 and 9 players.4 member from each club are randomly chosen to participate in a competition of two school.chosen player from one team are then randomly paired against chosen players of another team.suppose Rebecca and Elise are in two chess clubs of different school..what is the probability that<br />
<br />
1.Rebecca and Elise will be paired<br />
<br />
2.Rebecca and Elise will be chosen to play but they will NOT be paired against Each OtherProbabilityhttps://gateoverflow.in/123094/probability-exerciseFri, 31 Mar 2017 11:58:29 +0000Ravi asked his neighbor to water a delicate plant while he is away.
https://gateoverflow.in/122637/ravi-asked-his-neighbor-to-water-delicate-plant-while-he-away
Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability $4/5$ and with water, it would die with probability $3/20$. The probability that Ravi’s neighbor would remember to water the plant is $9/10$. If the plant actually died, what is the probability that Ravi’s neighbor forgot to water the plant?<br />
<br />
(A) $4/5$<br />
<br />
(B) $27/43$<br />
<br />
(C) $16/43$<br />
<br />
(D) $2/25$Probabilityhttps://gateoverflow.in/122637/ravi-asked-his-neighbor-to-water-delicate-plant-while-he-awaySun, 26 Mar 2017 23:16:01 +0000probability
https://gateoverflow.in/121747/probability
If from each box of the three boxes containing $3$ white and $3$ black,$2$ white and $2$ black,$1$ white and $3$ black,one ball is drawn at random ,then the probability that $2$ white and $1$ black ball will be drawn ?Probabilityhttps://gateoverflow.in/121747/probabilityThu, 16 Mar 2017 11:35:10 +0000probability
https://gateoverflow.in/121746/probability
There are $N$ persons sitting in a row. Two of them are selected at random.The probability that two selected persons are not together ?Probabilityhttps://gateoverflow.in/121746/probabilityThu, 16 Mar 2017 11:32:26 +0000probability
https://gateoverflow.in/121744/probability
There are four machines and it is known that exactly two of them are faulty .They are tested one by one in a random order till both the faulty machines are identified ,then the probability that only two tests are needed ?Probabilityhttps://gateoverflow.in/121744/probabilityThu, 16 Mar 2017 11:29:59 +0000Discrete Probability Doubt
https://gateoverflow.in/121501/discrete-probability-doubt
Consider a group of k people. Assume that each person's birthday is drawn uniformly at random from the 365 possibilities. (And ignore leap years.) What is the smallest value of ksuch that the expected number of pairs of distinct people with the same birthday is at least one?Combinatoryhttps://gateoverflow.in/121501/discrete-probability-doubtMon, 13 Mar 2017 21:10:18 +0000