GATE Overflow - Recent questions tagged probability
http://gateoverflow.in/tag/probability
Powered by Question2AnswerSheldon Ross Chapter 1 Example 3c
http://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.Combinatoryhttp://gateoverflow.in/134909/sheldon-ross-chapter-1-example-3cTue, 27 Jun 2017 06:52:14 +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 +0000Probability
http://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 Logichttp://gateoverflow.in/134654/probabilitySat, 24 Jun 2017 20:57:59 +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 +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 +0000IIITH-PGEE 2017
http://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.Probabilityhttp://gateoverflow.in/127525/iiith-pgee-2017Sun, 30 Apr 2017 18:24:00 +0000Probability
http://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?Probabilityhttp://gateoverflow.in/125997/probabilityMon, 17 Apr 2017 21:32:07 +0000Probability
http://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?Probabilityhttp://gateoverflow.in/125717/probabilitySat, 15 Apr 2017 21:04:10 +0000Probability
http://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>Probabilityhttp://gateoverflow.in/125714/probabilitySat, 15 Apr 2017 20:49:57 +0000Probability Exercise
http://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 OtherProbabilityhttp://gateoverflow.in/123094/probability-exerciseFri, 31 Mar 2017 11:58:29 +0000Ravi asked his neighbor to water a delicate plant while he is away.
http://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) $2/25$Probabilityhttp://gateoverflow.in/122637/ravi-asked-his-neighbor-to-water-delicate-plant-while-he-awaySun, 26 Mar 2017 23:16:01 +0000probability
http://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 ?Probabilityhttp://gateoverflow.in/121747/probabilityThu, 16 Mar 2017 11:35:10 +0000probability
http://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 ?Probabilityhttp://gateoverflow.in/121746/probabilityThu, 16 Mar 2017 11:32:26 +0000probability
http://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 ?Probabilityhttp://gateoverflow.in/121744/probabilityThu, 16 Mar 2017 11:29:59 +0000Discrete Probability Doubt
http://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?Combinatoryhttp://gateoverflow.in/121501/discrete-probability-doubtMon, 13 Mar 2017 21:10:18 +0000ISRO 2014- probability [EE]
http://gateoverflow.in/121207/isro-2014-probability-ee
80. A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is<br />
(A) 140<br />
(B) 196<br />
<br />
(C) 280<br />
<br />
(D) 346Probabilityhttp://gateoverflow.in/121207/isro-2014-probability-eeFri, 10 Mar 2017 15:30:50 +0000ISRO 2013- probability [EE]
http://gateoverflow.in/121198/isro-2013-probability-ee
Ten percent of screws produced in a certain factory turn out to be defective. Find the probability that in a sample of 10 screws chosen at random, exactly two will be defective.<br />
a) 0.2<br />
<br />
b) 0.25<br />
<br />
c) 0.8<br />
d) 0.3 79.Probabilityhttp://gateoverflow.in/121198/isro-2013-probability-eeFri, 10 Mar 2017 14:37:48 +0000ISRO 2013- Probability/Leap year [Mech]
http://gateoverflow.in/120893/isro-2013-probability-leap-year-mech
Chance that a leap year selected at random will contain 53 Sundays is<br />
(a) 3/7<br />
(b) 7/2<br />
(c) 7/3<br />
(d) 2/7Probabilityhttp://gateoverflow.in/120893/isro-2013-probability-leap-year-mechWed, 08 Mar 2017 09:15:25 +0000ISRO 2013- Probability [Mech]
http://gateoverflow.in/120891/isro-2013-probability-mech
If the probability for A to fail an examination is 0.2 and that for B is 0.3, then probability that either A of B fail is<br />
(a) 0.5<br />
(b) 0.06<br />
(c) 0.44<br />
(d) 0.38Probabilityhttp://gateoverflow.in/120891/isro-2013-probability-mechWed, 08 Mar 2017 09:12:42 +0000combinational circuit
http://gateoverflow.in/120518/combinational-circuit
Let combinational function $f(\text{a, b, c, d}) = \text{abc}'+\text{ab}'\text{cd}'$ (where $x'$ means complement of $x$). If all inputs are equally probable, then the probability that the function evaluates to True is:<br />
(A) 5/16<br />
(B) 1/4<br />
(C) 3/16<br />
(D) 1/8Digital Logichttp://gateoverflow.in/120518/combinational-circuitSat, 04 Mar 2017 15:02:44 +0000Probability
http://gateoverflow.in/120317/probability
The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student doesn't know the answer then the student guess the answer. The probability of the guess answer is being correct is 1/4.given that student has answer the questions correctly, the conditional probability that the student knows the correct answer isMathematical Logichttp://gateoverflow.in/120317/probabilityThu, 02 Mar 2017 22:18:07 +0000ISRO 2008- ECE Probability
http://gateoverflow.in/120242/isro-2008-ece-probability
A husband and wife appear in an interview for two vacancies for same post The. probability of husband getting selected is 1 /5 while the probability of wife getting selected is 1/7. Then the probability that anyone of them getting selected is<br />
<br />
a) 1 /35<br />
<br />
b) 11/35<br />
<br />
c) 12/35<br />
<br />
d) 34/35Probabilityhttp://gateoverflow.in/120242/isro-2008-ece-probabilityThu, 02 Mar 2017 13:22:19 +0000which os the following is not a valid probability density?
http://gateoverflow.in/120083/which-os-the-following-is-not-a-valid-probability-density
which os the following is not a valid probability density?<br />
<br />
-0.1<br />
<br />
1<br />
<br />
100<br />
<br />
1.1<br />
<br />
//this question is taken from one of the IIT kanpur interview experience blogs-Probabilityhttp://gateoverflow.in/120083/which-os-the-following-is-not-a-valid-probability-densityTue, 28 Feb 2017 22:55:53 +0000ISRO2012-ECE Probability
http://gateoverflow.in/119982/isro2012-ece-probability
Person X can solve 80% of the ISRO question paper and Person Y can solve 60%. The probability that at least one of them will solve a problem from the question paper, selected at random is :<br />
a. 0.48<br />
<br />
b. 0.70<br />
c. 0.88<br />
<br />
d. 0.92Probabilityhttp://gateoverflow.in/119982/isro2012-ece-probabilityTue, 28 Feb 2017 10:05:23 +0000probability
http://gateoverflow.in/119954/probability
i am not able to understand "when to use poisson random variable" concept comparing to other random variables ...can somebody explain ....Numerical Abilityhttp://gateoverflow.in/119954/probabilityMon, 27 Feb 2017 23:04:14 +0000probability
http://gateoverflow.in/119894/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15080373723529955280"></p>
<p>ANSWER I AM GETTING : <strong>(0.5) / [1-(0.5<sup>n</sup>)]</strong></p>
<p>ANSWER GIVEN : <strong>(0.5) / [ 1-(0.5<sup>n-1</sup>) ]</strong></p>Numerical Abilityhttp://gateoverflow.in/119894/probabilityMon, 27 Feb 2017 12:51:09 +0000sheldon ross
http://gateoverflow.in/119893/sheldon-ross
<p><strong>You know that a certain letter is equally likely to be in any one of three different folders. Let αi be the probability that you will find your letter upon making a quick examination of folder i if the letter is, in fact, in folder i, i = 1, 2, 3. (We may have αi < 1.) Suppose you look in folder 1 and do not find the letter. What is the probability that the letter is in folder 1?</strong></p>Probabilityhttp://gateoverflow.in/119893/sheldon-rossMon, 27 Feb 2017 12:49:54 +0000probability
http://gateoverflow.in/119891/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2183063912736234355"></p>Numerical Abilityhttp://gateoverflow.in/119891/probabilityMon, 27 Feb 2017 12:29:39 +0000probability
http://gateoverflow.in/119887/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16963734625635314674"></p>Numerical Abilityhttp://gateoverflow.in/119887/probabilityMon, 27 Feb 2017 11:14:52 +0000probability
http://gateoverflow.in/119842/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6016592354124857305"></p>Numerical Abilityhttp://gateoverflow.in/119842/probabilitySun, 26 Feb 2017 17:23:25 +0000probability
http://gateoverflow.in/119822/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5971067772582147941"></p>
<p>I am fine with (a)...which is 1/3....i am not able to understand b) and c) ....i feel answer as same for all 3 ...but answer given is different ....can anybody tell the difference between a) and b),c)</p>Numerical Abilityhttp://gateoverflow.in/119822/probabilitySun, 26 Feb 2017 14:00:22 +0000Probability
http://gateoverflow.in/119765/probability
There are 15 tennis balls in a box, of which 9 have not previously been used. Three of the balls are randomly chosen, played with, and then returned to the box. Later, another 3 balls are randomly chosen from the box. Find the probability that none of these balls has ever been used.Numerical Abilityhttp://gateoverflow.in/119765/probabilitySat, 25 Feb 2017 11:16:07 +0000probability
http://gateoverflow.in/119705/probability
In a bag,there are 4 fair coins and 3 unfair coins.The probability of getting a head in those unfair coins is 1/3 and tail is 2/3.Now if 2 coins are taken from the bag and flipped.What is the probability of getting both as heads ?Numerical Abilityhttp://gateoverflow.in/119705/probabilityThu, 23 Feb 2017 21:50:03 +0000#probability_doubt_in_basic_concept
http://gateoverflow.in/119694/%23probability_doubt_in_basic_concept
<p><span class="marker">1)</span> Two coins are tossed.What is the probability of getting one head and one tail ? WKT ANS IS 2/4=1/2</p>
<p><span class="marker">2)</span> A coin is tossed twice.What is the probability of getting one head and one tail ? WKT ANS is 2/4=1/2</p>
<p><span class="marker">3)</span> A bag has 3 red balls and 4 green balls.Two balls are picked from the bag randomly.What is the probability of getting one red and one green ? ANS GIVEN IS (3/7*4/6)....WHY NOT (3/7*4/6)+(4/7*3/6)</p>
<p>I MEAN WHY WE ARE CONSIDERING THE ORDER FOR<span class="marker"> 1)</span> AND <span class="marker">2)</span> BUT NOT FOR <span class="marker">3)</span></p>
<p>THAT IS IN <span class="marker">1)</span> AND <span class="marker">2)</span> ......{HEAD,TAIL} AND {TAIL,HEAD} ARE TREATED DIFFERENTLY BUT IN <span class="marker">3)</span> BOTH {R,G} AND {G,R} ARE TREATED SAME......WHY ???</p>
<p>please explain I am getting confused here ....</p>
<p> </p>Numerical Abilityhttp://gateoverflow.in/119694/%23probability_doubt_in_basic_conceptThu, 23 Feb 2017 17:17:04 +0000probability
http://gateoverflow.in/119660/probability
<p><img alt="" height="79" src="http://gateoverflow.in/?qa=blob&qa_blobid=15393637210555024677" width="638"></p>Probabilityhttp://gateoverflow.in/119660/probabilityWed, 22 Feb 2017 20:28:45 +0000ISRO2016 EC Probability
http://gateoverflow.in/119618/isro2016-ec-probability
<p>A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using public transport, further choice available are bus and metro. Out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded upto two decimals) of using a car, bus and metro respectively would be</p>
<hr>
<p>
<br>
(a) 0.45, 0.30 and 0.25</p>
<p>(b) 0.45, 0.25 and 0.30</p>
<p>(c) 0.45, 0.55 and 0</p>
<p>(d) 0.45, 0.35 and 0.20</p>
<p> </p>Probabilityhttp://gateoverflow.in/119618/isro2016-ec-probabilityWed, 22 Feb 2017 10:06:39 +0000probability
http://gateoverflow.in/119576/probability
If 4 married couples are arranged in a row, find the<br />
probability that no husband sits next to his wife.Numerical Abilityhttp://gateoverflow.in/119576/probabilityTue, 21 Feb 2017 20:57:05 +0000probability
http://gateoverflow.in/119574/probability
A closet contains 10 pairs of shoes. If 8 shoes<br />
are randomly selected, what is the probability that<br />
there will be exactly 1 complete pair?<br />
<br />
ANSWER I AM GETTING : [ C(10,1) * C(9,6) * 2^6 ] / [ C(20,8) ] <br />
ANSWER GIVEN : [ C(10,1) * C(9,6) * 2^6 ] / [C[20,8] *2!]<br />
<br />
PLEASE VERIFY IF AM MISSING SOMETHINGNumerical Abilityhttp://gateoverflow.in/119574/probabilityTue, 21 Feb 2017 20:51:49 +0000probability
http://gateoverflow.in/119570/probability
A group of 6 men and 6 women is randomly<br />
divided into 2 groups of size 6 each. What is the<br />
probability that both groups will have the same<br />
number of men?<br />
<br />
ANSWER I AM GETTING IS : [C(6,3) * C(6,3)] / [12!/(6!*6!*2!)]<br />
ANSWER GIVEN IS : [C(6,3) * C(6,3)] / [12!/(6!*6!)] <br />
source : sheldon m ross textbook<br />
<br />
please do verify and provide explanation ....<br />
what i feel is that "the answer should be divided by 2! because the permutations among 2 groups shouldnot happen because both the groups are unlabelled"Numerical Abilityhttp://gateoverflow.in/119570/probabilityTue, 21 Feb 2017 20:01:22 +0000probability
http://gateoverflow.in/119569/probability
Given 20 people, what is the probability that,<br />
among the 12 months in the year, there are 4<br />
months containing exactly 2 birthdays and 4 containing<br />
exactly 3 birthdays?Numerical Abilityhttp://gateoverflow.in/119569/probabilityTue, 21 Feb 2017 19:01:10 +0000probability
http://gateoverflow.in/119539/probability
How many people have to be in a room in order that the probability that at least two of them celebrate their birthday in the same month is at least $1/2$ ? Assume that all possible monthly outcomes are equally likely.Numerical Abilityhttp://gateoverflow.in/119539/probabilityTue, 21 Feb 2017 14:41:27 +0000probability
http://gateoverflow.in/119534/probability
Five people, designated as A, B, C, D, E, are<br />
arranged in linear order. Assuming that each possible<br />
order is equally likely, what is the probability<br />
that<br />
(a) there is exactly one person between A and B?<br />
(b) there are exactly two people between A<br />
and B?Numerical Abilityhttp://gateoverflow.in/119534/probabilityTue, 21 Feb 2017 13:49:01 +0000GATE2017-2-GA-5
http://gateoverflow.in/118419/gate2017-2-ga-5
<p>There are 3 red socks, 4 green socks and 3 blue socks. You choose 2 socks. The probability that they are of the same colour is</p>
<ol style="list-style-type: upper-alpha;">
<li>1/5</li>
<li>7/30</li>
<li>1/4</li>
<li>4/15</li>
</ol>Numerical Abilityhttp://gateoverflow.in/118419/gate2017-2-ga-5Tue, 14 Feb 2017 12:49:56 +0000GATE2017-1-GA-5
http://gateoverflow.in/118408/gate2017-1-ga-5
The probability that a $k$-digit number does NOT contain the digits 0, 5, or 9 is<br />
<br />
(A) $0.3^{k}$<br />
<br />
(B) $0.6^{k}$<br />
<br />
(C) $0.7^{k}$<br />
<br />
(D) $0.9^{k}$Numerical Abilityhttp://gateoverflow.in/118408/gate2017-1-ga-5Tue, 14 Feb 2017 12:47:38 +0000GATE2017-2-31
http://gateoverflow.in/118373/gate2017-2-31
<p>For any discrete random variable $X$, with probability mass function</p>
<p>$P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain discrete random variable $Y$, there exists a scalar $\beta \in [0,1]$ such that $g_y(z) = 1- \beta+\beta z)^N$. The expectation of $Y$ is</p>
<ol style="list-style-type:upper-alpha">
<li>$N \beta(1-\beta)$</li>
<li>$N \beta$</li>
<li>$N (1-\beta)$</li>
<li>Not expressible in terms of $N$ and $\beta$ alone</li>
</ol>
<p> </p>Probabilityhttp://gateoverflow.in/118373/gate2017-2-31Tue, 14 Feb 2017 12:43:16 +0000GATE2017-2-26
http://gateoverflow.in/118368/gate2017-2-26
<p>P and Q are considering to apply for a job. The probability that P applies for the job is 1/4, the probability that P applies for the job given that Q applies for the job is 1/2., and the probability that Q applies for the job given that P applies for the job is 1/3. Then the probability that P does not apply for the job given that Q does not apply for this job is</p>
<ol style="list-style-type: upper-alpha;">
<li>4/5</li>
<li>5/6</li>
<li>7/8</li>
<li>11/12</li>
</ol>Probabilityhttp://gateoverflow.in/118368/gate2017-2-26Tue, 14 Feb 2017 12:42:47 +0000