GATE Overflow - Recent questions tagged probability
http://gateoverflow.in/tag/probability
Powered by Question2Answerprobability
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 06:05:10 +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 06:02:26 +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 05:59:59 +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 15:40:18 +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 10:00:50 +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 09:07:48 +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 03:45:25 +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 03:42:42 +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 09:32:44 +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 16:48:07 +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 07:52:19 +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 17:25:53 +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 04:35:23 +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 17:34:14 +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 07:21:09 +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 07:19:54 +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 06:59:39 +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 05:44:52 +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 11:53:25 +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 08:30:22 +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 05:46:07 +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 16:20:03 +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 11:47:04 +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 14:58:45 +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 04:36:39 +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 15:27:05 +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 15:21:49 +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 14:31:22 +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 13:31:10 +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 09:11:27 +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 08:19:01 +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 07:19:56 +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 07:17:38 +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 07:13:16 +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 07:12:47 +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 07:05:42 +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 />
<br />
<br />
<br />
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 11:57:03 +0000gatebook
http://gateoverflow.in/116857/gatebook
In an examination there are 80 questions each having four choices. Exactly one of these four choices is correct and the other three are wrong. A student is awarded 1 mark for each correct answer, and -0.25 for each wrong answer. If a student ticks the answer of each question randomly, then the expected value of his/her total marks in the examination is.<br />
<br />
(A) -15<br />
<br />
(B) 0<br />
<br />
(C) 5<br />
<br />
(D) 20Probabilityhttp://gateoverflow.in/116857/gatebookTue, 07 Feb 2017 07:29:44 +0000GATE-2006-18
http://gateoverflow.in/115413/gate-2006-18
<p>We are given a set X = {x<sub>1</sub>, x<sub>2</sub> ...., x<sub>n</sub>} where x<sub>i</sub> = 2<sup>i</sup>. A sample S ⊆ X is drawn by selecting each x<sub>i</sub> independently with probability P<sub>i</sub> = $\frac{1}{2}$. The expected value of the smallest number in sample S is:</p>
<p>A) $\frac{1}{n}$</p>
<p>B) 2</p>
<p>C) $\sqrt{n}$</p>
<p>D) n</p>
<p> </p>Probabilityhttp://gateoverflow.in/115413/gate-2006-18Fri, 03 Feb 2017 15:47:57 +0000The Dice Game
http://gateoverflow.in/112103/the-dice-game
Three Players A, B and C play a game with a single die. The rules of<br />
the game are:<br />
Player A ALWAYS goes first.<br />
A rolls the die. If the die lands showing a 1 then A wins the game.<br />
If A does not throw a 1 then B has a turn.<br />
B rolls a die. If the die landing shows a 2 or 3 then B wins the<br />
game. If B does not throw a 2 or a 3 then C has a turn.<br />
<br />
C rolls the die. If the die lands showing a 4, 5 or 6 then C wins<br />
the game. If C does not throw a 4 or a 5 or a 6 then A starts again.<br />
<br />
This procedure continues until there is a winner.<br />
<br />
Investigate any or all of:<br />
<br />
1. The probabilities of each of A, B or C winning the game.<br />
<br />
2. Who will be the most likely winner?<br />
<br />
3. The most likely length of the game in terms of the number of rolls<br />
of the die to produce the winnerProbabilityhttp://gateoverflow.in/112103/the-dice-gameFri, 27 Jan 2017 17:31:09 +0000Probability
http://gateoverflow.in/111363/probability
A fair coin is tossed ten times in succession. If the first toss produces a head,<br />
then the probability of getting exactly three heads in ten tosses is<br />
<br />
I am doing like :-<br />
<br />
$\frac{1}{2}*n(9,2)*\frac{1}{2}^2\frac{1}{2}^7$<br />
<br />
I am using bionomial distribution here,Now for initial first head,will probability will be (1/2) or will it be 1?It says first produces head,means first head probability is (1/2) or is it (1)?<br />
<br />
After that i will find 2 success if of 9 trials.<br />
<br />
Please help,that inital (1/2) term above is correct ir should it be 1?Probabilityhttp://gateoverflow.in/111363/probabilityThu, 26 Jan 2017 02:41:18 +0000Probability
http://gateoverflow.in/110852/probability
A,B,C and D are four players playing the dice game and who gets the number 5 first wins the game. If A starts first what is the probability that D wins the game in second trail isProbabilityhttp://gateoverflow.in/110852/probabilityWed, 25 Jan 2017 08:52:07 +0000Probability
http://gateoverflow.in/110683/probability
<p><em>Given below are two problems that I had encountered in two different tests. They seem to me as the same type. However, the solutions provided have been done differently. Where am I wrong?</em></p>
<p><em><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6229195413004414913"></em></p>Probabilityhttp://gateoverflow.in/110683/probabilityTue, 24 Jan 2017 19:26:36 +0000RD SHARMA
http://gateoverflow.in/110397/rd-sharma
There are 4 white and 4 black balls in a bag and 3 balls are drawn at random.If balls of same colour are identical,the probability that none of them are black is,(I am getting 1/14,ans is 1/4)Probabilityhttp://gateoverflow.in/110397/rd-sharmaTue, 24 Jan 2017 10:12:35 +0000Made Easy test series
http://gateoverflow.in/109586/made-easy-test-series
Fifteen coupons are numbered from 1 to 15. Seven coupons are selected at random one at a time with replacement. What is the probability that the largest number appearing on a selected coupon is 9 ?<br />
<br />
<br />
<br />
The solution provided is (3/5)^7 but from the language of question I think there must be at least one 9 <br />
<br />
hence I think the solution should be $\frac{9^{7}-8^{7}}{15^{7}}$Probabilityhttp://gateoverflow.in/109586/made-easy-test-seriesMon, 23 Jan 2017 08:06:26 +0000probability
http://gateoverflow.in/107943/probability
Consider four coins, three of which are fair, that is they have heads on one side and tails on the other and both are equally likely to occur in a toss. The fourth coin has tails on both sides. Given that one coin amongst the four is picked at random and is tossed, and the outcome is seen to be tail, what is the probability that its other side is headsProbabilityhttp://gateoverflow.in/107943/probabilityThu, 19 Jan 2017 12:37:58 +0000probability
http://gateoverflow.in/107872/probability
If two cards are drawn from a pack of 52 cards, which are diamonds. Using Poissons distribution find the probability of getting two diamonds at least 3 times in 51 consecutive trials of two cards drawing each time _________Probabilityhttp://gateoverflow.in/107872/probabilityThu, 19 Jan 2017 09:05:53 +0000virtual-gate-2017
http://gateoverflow.in/107733/virtual-gate-2017
<p>A country’s GDP grew by 7.8% within a period. During the same period the country’s per-capita-GDP (= ratio of GDP to the total population) increased by 10%. During this period, the total population of the country</p>
<p>
</p>
<table>
<thead>
<tr>
<th> </th>
<th> </th>
</tr>
</thead>
<tbody>
<tr>
<td> </td>
<td>
<p>(A) increased by 4%</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(B) decreased by 4%</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(C) increased by 2%</p>
</td>
</tr>
<tr>
<td> </td>
<td>
<p>(D) decreased by 2%</p>
</td>
</tr>
</tbody>
</table>
Numerical Abilityhttp://gateoverflow.in/107733/virtual-gate-2017Thu, 19 Jan 2017 01:02:18 +0000Virtual Gate 2016-mock-1 Question 55
http://gateoverflow.in/107383/virtual-gate-2016-mock-1-question-55
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9340021440225560575"></p>Computer Networkshttp://gateoverflow.in/107383/virtual-gate-2016-mock-1-question-55Wed, 18 Jan 2017 08:54:07 +0000Virtual Gate 2016-mock-1 Question 37
http://gateoverflow.in/107380/virtual-gate-2016-mock-1-question-37
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12401454171743204172"></p>Probabilityhttp://gateoverflow.in/107380/virtual-gate-2016-mock-1-question-37Wed, 18 Jan 2017 08:51:55 +0000