GATE Overflow - Recent questions in Probability
http://gateoverflow.in/questions/mathematics/probability
Powered by Question2AnswerProbability 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 +0000ISI 2015 MMA 7
http://gateoverflow.in/129269/isi-2015-mma-7
Suppose X is distributed as Poisson with mean λ. Then E(1/(X + 1)) is<br />
<br />
(A) $\frac{e^{\lambda }-1}{\lambda }$ <br />
<br />
(B) $\frac{e^{\lambda }-1}{\lambda +1}$<br />
<br />
(C) $\frac{1-e^{-\lambda }}{\lambda}$ <br />
<br />
(D) $\frac{1-e^{-\lambda }}{\lambda + 1}$Probabilityhttp://gateoverflow.in/129269/isi-2015-mma-7Thu, 11 May 2017 10:08:34 +0000#probability
http://gateoverflow.in/128939/%23probability
8 pairs of shoes are in a closet. 8 shoes are selected at random. The probability that there will be at least one pair and at most 3 pairs amongst selected shoes are?Probabilityhttp://gateoverflow.in/128939/%23probabilityMon, 08 May 2017 19:11:08 +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 +0000Explanation needed!!
http://gateoverflow.in/123899/explanation-needed
<p>You roll a fair four-sided die. If the result is 1 or 2, you roll once
<br>
more but otherwise, you stop. What is the probability that the sum total of your
<br>
rolls is at least 4?</p>
<ol>
<li>9/8</li>
<li>9/16</li>
<li>3/5</li>
<li>1/16</li>
</ol>
<p> </p>Probabilityhttp://gateoverflow.in/123899/explanation-neededTue, 04 Apr 2017 10:39:42 +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 +0000The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3
http://gateoverflow.in/121854/probability-that-hits-target-probability-that-hits-target
The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3 .<br />
If each fires once and the target is hit only once, what is the probability that A hits the target?Probabilityhttp://gateoverflow.in/121854/probability-that-hits-target-probability-that-hits-targetThu, 16 Mar 2017 20:56:15 +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 +0000MEBook
http://gateoverflow.in/121682/mebook
Assume that a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time.So find the probability that the aggregate of total of values that turn up is at least 6?Probabilityhttp://gateoverflow.in/121682/mebookWed, 15 Mar 2017 18:25:51 +0000probability
http://gateoverflow.in/121543/probability
A man takes a step forward with probability 0.4 and backwards with probability 0.6 .find the probability that at the end of eleven steps he is just one step away from the starting pointProbabilityhttp://gateoverflow.in/121543/probabilityTue, 14 Mar 2017 11:38:44 +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 [EE]
http://gateoverflow.in/121197/isro-2013-probability-ee
An urn contains 5 black and 5 white balls. The probability of drawing two balls of the same colour<br />
<br />
a) 2/9<br />
<br />
b) 4/9<br />
<br />
c) 1/9<br />
<br />
d) 5/9Probabilityhttp://gateoverflow.in/121197/isro-2013-probability-eeFri, 10 Mar 2017 14:36:31 +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 +0000ISRO 2014- Probability [Mech]
http://gateoverflow.in/120812/isro-2014-probability-mech
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?<br />
<br />
<br />
a) 70/82<br />
<br />
b) 35/70<br />
<br />
c) 41/82<br />
<br />
d) 41/70Probabilityhttp://gateoverflow.in/120812/isro-2014-probability-mechTue, 07 Mar 2017 15:51:31 +0000ISRO 2015- probability [Mech]
http://gateoverflow.in/120801/isro-2015-probability-mech
The probability that a teacher will give an unannounced test during any class is 1/5. If a student is absent twice, then probability that misses at least one test is<br />
<br />
(a) 24/25<br />
<br />
(b) 16/25<br />
<br />
(c) 7/25<br />
<br />
(d) 9/25Probabilityhttp://gateoverflow.in/120801/isro-2015-probability-mechTue, 07 Mar 2017 15:24:57 +0000ISRO 2016 Probability [Mech]
http://gateoverflow.in/120796/isro-2016-probability-mech
A and B are two candidates appearing for an interview by a company. The probability that A is selected is 0.5 and the probability that both A and B are selected is at most 0.3. The probability of B getting selected is<br />
<br />
<br />
<br />
(a) 0.9<br />
<br />
(b) 5 0.3<br />
<br />
(c) S 0.6<br />
<br />
(d) 0.5Probabilityhttp://gateoverflow.in/120796/isro-2016-probability-mechTue, 07 Mar 2017 15:03:22 +0000ISRO 2016 Number of trials [Mech]
http://gateoverflow.in/120795/isro-2016-number-of-trials-mech
There are 20 locks and 20 matching keys. Maximum number of trials required to match all the locks is<br />
<br />
(a) 190<br />
<br />
(b) 210<br />
<br />
(c) 400<br />
<br />
(d) 40Probabilityhttp://gateoverflow.in/120795/isro-2016-number-of-trials-mechTue, 07 Mar 2017 15:01:05 +0000ISRO 2012- Probability [Mech]
http://gateoverflow.in/120790/isro-2012-probability-mech
The probability that A happens is 1/3. the odds against happening A are:<br />
<br />
a) 2:1<br />
<br />
b) 3:2<br />
<br />
c) 1:2<br />
<br />
d) 2:3Probabilityhttp://gateoverflow.in/120790/isro-2012-probability-mechTue, 07 Mar 2017 14:37:04 +0000ISRO 2012: MEch Probability
http://gateoverflow.in/120771/isro-2012-mech-probability
Let E and F be any two events with P(E U F)= 0.8, P(E) = 0.4 and P (E/ F) = 0.3. Then P (F) is <br />
<br />
(a) 3/7<br />
<br />
(b) 4/7<br />
(c) 3/5<br />
<br />
(d) 2/5Probabilityhttp://gateoverflow.in/120771/isro-2012-mech-probabilityTue, 07 Mar 2017 12:22:15 +0000Probability
http://gateoverflow.in/120760/probability
There are two Biased dice of which first dice shows an even number twice as frequently as odd number second dice shows 5, thrice as frequently is any other number. If these dice are rolled together what is the probability of getting---<br />
<br />
1)Sum as 10<br />
<br />
2)Sum more than 10.Probabilityhttp://gateoverflow.in/120760/probabilityTue, 07 Mar 2017 11:47:41 +0000TIFR 2012- Probability
http://gateoverflow.in/120512/tifr-2012-probability
<p>Amar and Akbar both tell the truth with probability 3/4 and lie with probability 1/4. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "<strong>Amar told me that India won</strong>".</p>
<p>What probability should Anthony assign to India's win?</p>
<p>(a) 9/16</p>
<p>(b) 6/16</p>
<p>(c) 7/16</p>
<p>(d) 10/16</p>
<p> </p>Probabilityhttp://gateoverflow.in/120512/tifr-2012-probabilitySat, 04 Mar 2017 13:30:10 +0000ISRO 2006- ECE Probability
http://gateoverflow.in/120495/isro-2006-ece-probability
A box contains 5 black and 5 red balls. Two balls are one after another from the box, without replacement. both balls being red is<br />
<br />
a) 1/90<br />
<br />
b) 1/5<br />
<br />
c) 19/90<br />
<br />
d) 2/9Probabilityhttp://gateoverflow.in/120495/isro-2006-ece-probabilitySat, 04 Mar 2017 11:12:51 +0000ISRO 2007- ECE Probability
http://gateoverflow.in/120401/isro-2007-ece-probability
<p>A bag contains eight white and six red marbles. The probability of drawing two marbles of same colour is</p>
<p>a) 8c<sub>2</sub> .6c<sub>2</sub> / 14c<sub>2</sub> </p>
<p>b) 8c<sub>2</sub> /14c<sub>2</sub> + 6c<sub>2</sub> /14c<sub>2</sub></p>
<p>c) 8c<sub>2</sub>.6c<sub>2</sub> /14c<sub>2</sub>.14c<sub>2</sub></p>
<p>d)8c<sub>2</sub> /14c<sub>2</sub> + 6c<sub>2</sub> /12c<sub>2</sub></p>Probabilityhttp://gateoverflow.in/120401/isro-2007-ece-probabilityFri, 03 Mar 2017 12:07:47 +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 +0000ISRO 2009-ECE Probability
http://gateoverflow.in/120116/isro-2009-ece-probability
A man with n keys wants to open a lock. He tries his keys at random. The expected number of attempts for his success is (keys are replaced after every attempt)<br />
<br />
a) n/2<br />
<br />
b) n<br />
<br />
c) √ n<br />
<br />
d) None of the aboveProbabilityhttp://gateoverflow.in/120116/isro-2009-ece-probabilityWed, 01 Mar 2017 09:50:26 +0000ISRO 2009- ECE Engineering Mathematics
http://gateoverflow.in/120110/isro-2009-ece-engineering-mathematics
A straight line and a circle of radius a are given. A chord is drawn at random to this circle parallel to the given line. Expected length of the chord is<br />
a) 2a<br />
<br />
b) π a<br />
c) π a/2<br />
<br />
d) None of the aboveProbabilityhttp://gateoverflow.in/120110/isro-2009-ece-engineering-mathematicsWed, 01 Mar 2017 09:33:13 +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 +0000ISRO 2012- ECE Probability
http://gateoverflow.in/119980/isro-2012-ece-probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6065700306588137035"></p>
<p> </p>
<p>a) 0 &1</p>
<p>b) 1&2</p>
<p>c) 1&4</p>
<p>d) None of these</p>Probabilityhttp://gateoverflow.in/119980/isro-2012-ece-probabilityTue, 28 Feb 2017 09:56:48 +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/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 +0000ISRO2014-EC Mathematics
http://gateoverflow.in/119647/isro2014-ec-mathematics
<p>Match the following:</p>
<p>A Gaussian distribution 1 Calls on a telephone channel</p>
<p>B Rayleigh distribution 2 Random number</p>
<p>C Poisson distribution 3 Thermal noise</p>
<p>D Uniform distribution 4 Fading channel in wireless communication</p>
<hr>
<p>
<br>
A) A-3, B-1, C-4, D-2</p>
<p>B) A-3, B-4, C-2, D-1</p>
<p>C) A-1, B-4, C-3, D-2</p>
<p>D) A-3, B-4, C-1, D-2</p>
<p> </p>Probabilityhttp://gateoverflow.in/119647/isro2014-ec-mathematicsWed, 22 Feb 2017 15:53:36 +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 +0000ISI 2016A1
http://gateoverflow.in/119499/isi-2016a1
A standard deck of cards, containing 13 cards in each of 4 suites,<br />
is distributed equally among 4 players.<br />
(a) Show that each player must have at least 4 cards of the same<br />
suite. [5]<br />
(b) Define data structures to represent (i) the deck of cards, and<br />
(ii) a distribution of the cards to the four players. [5]<br />
(c) Using your data structures, write an algorithm which<br />
distributes the deck of cards one by one to the four<br />
players in a cyclical manner. [5Probabilityhttp://gateoverflow.in/119499/isi-2016a1Mon, 20 Feb 2017 21:53:14 +0000GATE2017-2-48
http://gateoverflow.in/118513/gate2017-2-48
<p>If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)<sup>2</sup>] equals ___.</p>Probabilityhttp://gateoverflow.in/118513/gate2017-2-48Tue, 14 Feb 2017 14:01:08 +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 +0000GATE2017-1-19
http://gateoverflow.in/118299/gate2017-1-19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $max\left ( X,0 \right )$ where $max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .Probabilityhttp://gateoverflow.in/118299/gate2017-1-19Tue, 14 Feb 2017 12:35:42 +0000Probability
http://gateoverflow.in/117354/probability
Three $N$ bit binary strings $S_1$,$S_2$,$S_3$ are selected in random. What is the probability that result of bit-wise XOR among them contains $k$ $1$'s.i.e. $S_1\oplus S_2\oplus S_3$ = $S$ , No of set bits in $S$ = $k$<br />
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is it $\binom{n}{k}\left ( \frac{1}{2} \right )^k\left ( \frac{1}{2} \right )^{n-k}$ ??Probabilityhttp://gateoverflow.in/117354/probabilityWed, 08 Feb 2017 17:27:03 +0000