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<p><strong>A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum no. of marbles you have to choose randomly from the bag to ensure that we get 4 marbles of same color?</strong></p>Probabilityhttp://gateoverflow.in/155166/doubtTue, 26 Sep 2017 02:49:37 +0000Probability
http://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 ?Probabilityhttp://gateoverflow.in/155136/probabilityMon, 25 Sep 2017 18:30:19 +0000sheldon ross
http://gateoverflow.in/154985/sheldon-ross
Consider the following technique for shuffling a<br />
deck of n cards: For any initial ordering of the<br />
cards, go through the deck one card at a time and<br />
at each card, flip a fair coin. If the coin comes<br />
up heads, then leave the card where it is; if the<br />
coin comes up tails, then move that card to the<br />
end of the deck. After the coin has been flipped n<br />
times, say that one round has been completed. For<br />
instance, if n = 4 and the initial ordering is 1, 2, 3,<br />
4, then if the successive flips result in the outcome<br />
h, t, t, h, then the ordering at the end of the round<br />
is 1, 4, 2, 3. Assuming that all possible outcomes of<br />
the sequence of n coin flips are equally likely, what<br />
is the probability that the ordering after one round<br />
is the same as the initial ordering?Probabilityhttp://gateoverflow.in/154985/sheldon-rossMon, 25 Sep 2017 07:06:06 +0000Sheldon Ross chapter#3 Qno-45
http://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>Probabilityhttp://gateoverflow.in/153765/sheldon-ross-chapter%233-qno-45Wed, 20 Sep 2017 17:38:27 +0000Sheldon ross chapter#3 Qno -30
http://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?Probabilityhttp://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30Tue, 19 Sep 2017 11:01:23 +0000sheldon M ross 4 ed - chapter-3 qno- 25
http://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?Probabilityhttp://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25Mon, 18 Sep 2017 09:01:47 +0000MA 2017
http://gateoverflow.in/152981/ma-2017
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4719585218381730416"></p>Probabilityhttp://gateoverflow.in/152981/ma-2017Sun, 17 Sep 2017 16:48:27 +0000MA 2013
http://gateoverflow.in/152979/ma-2013
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11554834656157963260"></p>Probabilityhttp://gateoverflow.in/152979/ma-2013Sun, 17 Sep 2017 16:44:37 +0000MA 2013 MA
http://gateoverflow.in/152978/ma-2013-ma
Let X be an arbitrary random variable that takes values in {0,1,…,10}. The minimum and maximum possible values of the variance of X are<br />
<br />
(A) 0 and 30<br />
<br />
(B) 1 and 30<br />
<br />
(C) 0 and 25<br />
<br />
(D) 1 and 25<br />
<br />
GIVEN ANSWER IS CProbabilityhttp://gateoverflow.in/152978/ma-2013-maSun, 17 Sep 2017 16:42:44 +0000MA 2014
http://gateoverflow.in/152977/ma-2014
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=173441506922385334"></p>Probabilityhttp://gateoverflow.in/152977/ma-2014Sun, 17 Sep 2017 16:41:46 +0000MA 2014
http://gateoverflow.in/152976/ma-2014
The time to failure, in months, of light bulbs manufactured at two plants A and B obey the exponential distribution with means 6 and 2 months respectively. Plant B produces four times as many bulbs as plant A does. Bulbs from these plants are indistinguishable. They are mixed and sold together. Given that a bulb purchased at random is working after 12 months, the probability that it was manufactured at plant A is _____<br />
<br />
GIVEN ANSWER: 0.92 to 0.94Probabilityhttp://gateoverflow.in/152976/ma-2014Sun, 17 Sep 2017 16:40:39 +0000Probability doubt
http://gateoverflow.in/152779/probability-doubt
Three numbers are chosen at random without replacement from {1,2,3,.....,8}. What is the probability that minimum is 3 given that their maximum is 6?Probabilityhttp://gateoverflow.in/152779/probability-doubtSun, 17 Sep 2017 02:50:02 +0000Probability doubt
http://gateoverflow.in/152641/probability-doubt
A box contains 3 coins: two regular coins and one fake two headed P(H )= 1 .you pick up one at random and toss it and gets heads.the probability that it is a two headed coin is....Probabilityhttp://gateoverflow.in/152641/probability-doubtSat, 16 Sep 2017 11:54:26 +0000GATE 2012 MA
http://gateoverflow.in/152551/gate-2012-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2887404449711765735"></p>
<p>ANSWER GIVEN 0.73-0.77</p>Probabilityhttp://gateoverflow.in/152551/gate-2012-maSat, 16 Sep 2017 06:31:05 +0000GATE 2017 MA
http://gateoverflow.in/152549/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9673049504830691856"></p>
<p>ANSWER GIVEN IS 0.27-0.37</p>Probabilityhttp://gateoverflow.in/152549/gate-2017-maSat, 16 Sep 2017 06:28:47 +0000GATE 2017 MA
http://gateoverflow.in/152545/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7133725661348086680"></p>
<p>ANSWER GIVEN IS 4</p>Probabilityhttp://gateoverflow.in/152545/gate-2017-maSat, 16 Sep 2017 06:25:02 +0000GATE 2017 MA
http://gateoverflow.in/152544/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6913064227682912036"></p>
<p>Answer given is D</p>Probabilityhttp://gateoverflow.in/152544/gate-2017-maSat, 16 Sep 2017 06:22:07 +0000GATE 2015 MA
http://gateoverflow.in/152542/gate-2015-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6891829485658445850"></p>Probabilityhttp://gateoverflow.in/152542/gate-2015-maSat, 16 Sep 2017 06:18:02 +0000probability
http://gateoverflow.in/152420/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7189816802564820416"></p>Probabilityhttp://gateoverflow.in/152420/probabilityFri, 15 Sep 2017 15:59:31 +0000GATE 2015 MA
http://gateoverflow.in/152364/gate-2015-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10236012100461470116"></p>Probabilityhttp://gateoverflow.in/152364/gate-2015-maFri, 15 Sep 2017 10:50:06 +0000GATE 2016 MA
http://gateoverflow.in/152362/gate-2016-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10576038349030577104"></p>
<p>THE GIVEN ANSWER KEY IS 0.65 to 0.71 I AM GETTING 0.40...</p>Probabilityhttp://gateoverflow.in/152362/gate-2016-maFri, 15 Sep 2017 10:48:10 +0000Probability doubt
http://gateoverflow.in/151117/probability-doubt
A box contains 10 red balls and 15 Blue Balls.One ball is lost. Two balls are drawn from box and are found to be red ones.Find the chance that the missing ball is blue ball.<br />
<br />
a)15/23<br />
<br />
b)0.347<br />
<br />
c)0.6<br />
<br />
d)noneProbabilityhttp://gateoverflow.in/151117/probability-doubtSun, 10 Sep 2017 04:53:48 +0000Expectation
http://gateoverflow.in/150904/expectation
Let A[1:n] be an array such that A[i]=i . An algorithm randomly permutes the elements of A, call the resulting array A' . Let X denote the number of location such that A'[i]=i. What is expectation of X?Probabilityhttp://gateoverflow.in/150904/expectationSat, 09 Sep 2017 09:30:56 +0000Normal Distribution
http://gateoverflow.in/150896/normal-distribution
The median of a normal variate x with probablity dessity function<br />
<br />
f(x) = 1/(sigma*root(2*pi)*exp[-{(x-u)^2}/(2*sigma^2)] = ?Probabilityhttp://gateoverflow.in/150896/normal-distributionSat, 09 Sep 2017 08:56:07 +0000EC,GATE2007
http://gateoverflow.in/148992/ec-gate2007
<p>An examination consists of two papers , paper1 and paper2 . the probability of failing in paper 1 is 0.3 and that in paper 2 is 0.2 . Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6 .The probability of student failing in both papers is ...?
<br>
<br>
ans : 0.12 ...
<br>
<br>
now i simply got the ans by putting values in formula ... no problem , but i tried with other methed
<br>
<br>
i just creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8471425614467305877"></p>Probabilityhttp://gateoverflow.in/148992/ec-gate2007Fri, 01 Sep 2017 05:23:33 +0000#first course in probability #sheldon_ross 8th edition Qn. #12(a)
http://gateoverflow.in/148961/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2312
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if (a) a student can receive any number of awards?Probabilityhttp://gateoverflow.in/148961/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2312Fri, 01 Sep 2017 02:51:15 +0000#first course in probability #sheldon_ross 8th edition Qn. #10(c)
http://gateoverflow.in/148951/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2310
In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?Probabilityhttp://gateoverflow.in/148951/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2310Fri, 01 Sep 2017 02:18:18 +0000#first course in probability #sheldon_ross 8th edition Chapter 1 ,question 4
http://gateoverflow.in/148948/%23first-probability-%23sheldon_ross-edition-chapter-question
John, Jim, Jay, and Jack have formed a band consisting of 4 instruments. If each of the boys can play all 4 instruments, how many different arrangements are possible? What if John and Jim can play all 4 instruments, but Jay and Jack can each play only piano and drums?Probabilityhttp://gateoverflow.in/148948/%23first-probability-%23sheldon_ross-edition-chapter-questionFri, 01 Sep 2017 01:40:08 +0000Probability
http://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?Probabilityhttp://gateoverflow.in/148385/probabilityWed, 30 Aug 2017 03:56:33 +0000probability
http://gateoverflow.in/144372/probability
<p><img alt="" height="201" src="http://gateoverflow.in/?qa=blob&qa_blobid=3799245635594239058" width="652"></p>Probabilityhttp://gateoverflow.in/144372/probabilityTue, 15 Aug 2017 13:28:46 +0000Probability Gate EE 2016
http://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 _________.Probabilityhttp://gateoverflow.in/143924/probability-gate-ee-2016Sun, 13 Aug 2017 18:59:07 +0000introduction to engineering mathematics volume 3 by h.k. dass
http://gateoverflow.in/143912/introduction-to-engineering-mathematics-volume-3-by-h-dass
Three machines I,II,III manufacture respectively 0.4,0.5,0.1 of the total production.The percentage of defective items produced by I,II,III is 2,4,1 percent respectively.for an item chosen at random ,what is the probability that it is defective ?Probabilityhttp://gateoverflow.in/143912/introduction-to-engineering-mathematics-volume-3-by-h-dassSun, 13 Aug 2017 18:23:21 +0000SELF MADE
http://gateoverflow.in/141214/self-made
10 distinct accident occurs in a week.What is the probability that all accidents occured on the same day ?Probabilityhttp://gateoverflow.in/141214/self-madeWed, 02 Aug 2017 10:34:09 +0000Conditional Probability
http://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 AProbabilityhttp://gateoverflow.in/141030/conditional-probabilityTue, 01 Aug 2017 10:45:25 +0000probability
http://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?Probabilityhttp://gateoverflow.in/137763/probabilityFri, 14 Jul 2017 09:19:07 +0000probability
http://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?Probabilityhttp://gateoverflow.in/137762/probabilityFri, 14 Jul 2017 09:18:35 +0000probability
http://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>Probabilityhttp://gateoverflow.in/137217/probabilityTue, 11 Jul 2017 09:10:49 +0000Doubt
http://gateoverflow.in/136941/doubt
What is mode of 1,2,3,3,4,4 ?Probabilityhttp://gateoverflow.in/136941/doubtSun, 09 Jul 2017 15:06:37 +0000Probability posion distribtuion
http://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.).1439Probabilityhttp://gateoverflow.in/135554/probability-posion-distribtuionSat, 01 Jul 2017 07:43:11 +0000Gate EE 17
http://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 _________Probabilityhttp://gateoverflow.in/135069/gate-ee-17Wed, 28 Jun 2017 10:26:41 +0000[Gate 2006 EC] Probability
http://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>Probabilityhttp://gateoverflow.in/134674/gate-2006-ec-probabilitySun, 25 Jun 2017 06:07:49 +0000IISc PhD
http://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?Probabilityhttp://gateoverflow.in/132635/iisc-phdSun, 11 Jun 2017 07:18:42 +0000Sheldon Ross chapter 2 questions 26
http://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).Probabilityhttp://gateoverflow.in/132384/sheldon-ross-chapter-2-questions-26Fri, 09 Jun 2017 05:26:43 +0000sheldon ross, chapter 2, question 17
http://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.Probabilityhttp://gateoverflow.in/132359/sheldon-ross-chapter-2-question-17Fri, 09 Jun 2017 01:32:42 +0000Probability of dice
http://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)Probabilityhttp://gateoverflow.in/131870/probability-of-diceSun, 04 Jun 2017 17:00:17 +0000ACE Practice Test question
http://gateoverflow.in/131760/ace-practice-test-question
An electronic assembly consists of two sub systems say A and B from previous testing procedures , the following probability are assumed to be known,<br />
<br />
P(A fails) = 0.2<br />
<br />
P(B fails alone) = 0.15<br />
<br />
P (A and B fail) = 0.15<br />
<br />
then the conditional probability P(A fails| B has failed) =Probabilityhttp://gateoverflow.in/131760/ace-practice-test-questionSat, 03 Jun 2017 14:30:09 +0000Probability puzzles
http://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?Probabilityhttp://gateoverflow.in/130530/probability-puzzlesTue, 23 May 2017 10:21:01 +0000Probbility puzzles
http://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?Probabilityhttp://gateoverflow.in/130529/probbility-puzzlesTue, 23 May 2017 10:08:48 +0000Rosen Discreate Probability
http://gateoverflow.in/130478/rosen-discreate-probability
Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 99.9% of people with the disease test positive and only 0.02% who do not have the disease test positive.<br />
<br />
a) What is the probability that someone who tests positive has the genetic disease?<br />
<br />
b) What is the probability that someone who tests negative does not have the disease?<br />
<br />
My Answers :-<br />
<br />
P(D) = 0.00001 <br />
<br />
P(D') = 0.99999<br />
<br />
P(P/D) = 0.999<br />
<br />
P(P'/D) = 0.001<br />
<br />
P(P/D') = 0.0002<br />
<br />
P(P'/D') = 0.9998<br />
<br />
Answer a) $\frac{(0.999)(0.00001)}{(0.999)(0.00001) + (0.0002)(0.99999)}$<br />
<br />
Answer b) $\frac{(0.9998)(0.99999)}{(0.9998)(0.99999) + (0.001)(0.00001)}$<br />
<br />
Correct me if I am wrong?Probabilityhttp://gateoverflow.in/130478/rosen-discreate-probabilityMon, 22 May 2017 16:34:47 +0000counting
http://gateoverflow.in/130233/counting
Number of words of 4 letters that can be formed with the letters of the word IITJEE is<br />
<br />
a) 42 b) 82 c)102 d) 142Probabilityhttp://gateoverflow.in/130233/countingSat, 20 May 2017 12:04:28 +0000