GATE Overflow - Recent questions tagged conditional-probability
http://gateoverflow.in/tag/conditional-probability
Powered by Question2AnswerProbability fair and unfair coin together
http://gateoverflow.in/138892/probability-fair-and-unfair-coin-together
<p>How to solve this question.</p>
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<p>A box contains 5 fair coins and 5 biased coins. Each biased coin has a probability of a head 4/5. A coin is drawn at random from the box and tossed. Then a second coin is drawn at random from the box (without replacing the first one.) Given that the first coin has shown head, the conditional probability that the second coin is fair, is </p>
<p>a) 20/39</p>
<p>b) 20/37</p>
<p>c) 1/2</p>
<p>d) 7/13</p>Databaseshttp://gateoverflow.in/138892/probability-fair-and-unfair-coin-togetherThu, 20 Jul 2017 13:43:34 +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 +0000TIFR 2012- Probability
http://gateoverflow.in/120512/tifr-2012-probability
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, "Amar told me that India won".<br />
<br />
What probability should Anthony assign to India's win?<br />
<br />
(a) 9/16<br />
<br />
(b) 6/16<br />
<br />
(c) 7/16<br />
<br />
(d) 10/16Probabilityhttp://gateoverflow.in/120512/tifr-2012-probabilitySat, 04 Mar 2017 13:30:10 +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 +0000Maths
http://gateoverflow.in/96482/maths
There are 2 white and 4 black balls in urn A; in urn B, there are 4 white and 7 black balls. If one ball is randomly replaced from A into B and a ball is drawn from B then find the probability for the ball to be a white one?Probabilityhttp://gateoverflow.in/96482/mathsSun, 25 Dec 2016 13:21:58 +0000conditional probability
http://gateoverflow.in/62133/conditional-probability
A box contains 10 mangoes out of which 4 are rotten .Two mangoes are taken out together. If one of them is found to be good ,then find the probability other is also goodProbabilityhttp://gateoverflow.in/62133/conditional-probabilitySun, 07 Aug 2016 05:06:03 +0000conditional probability
http://gateoverflow.in/62131/conditional-probability
One dice is thrown three times and the sum of the thrown numbers is 15.find the probability for which number 4 appears in first throw.Probabilityhttp://gateoverflow.in/62131/conditional-probabilitySun, 07 Aug 2016 04:45:52 +0000ISRO2007-33
http://gateoverflow.in/49507/isro2007-33
<p>Company X shipped 5 computer chips, 1 of which was defective. and company Y shipped 4 computer chips, 2 of which were defective. One computer chip is to be chosen uniformly at a random from the 9 chips shipped by the companies. If the chosen chip is found to be defective, what is the probability that the chip came from the company Y?</p>
<ol style="list-style-type: upper-alpha;">
<li>2/9</li>
<li>4/9</li>
<li>2/3</li>
<li>1/2</li>
</ol>
Probabilityhttp://gateoverflow.in/49507/isro2007-33Fri, 10 Jun 2016 07:15:42 +0000CMI2013-A-02
http://gateoverflow.in/46592/cmi2013-a-02
<p>10% of all email you receive is spam. Your spam filter is 90% reliable: that is, 90% of the mails it marks as spam are indeed spam and 90% of spam mails are correctly labelled as spam. If you see a mail marked spam by your filter, what is the probability that it really is spam?</p>
<ol style="list-style-type: upper-alpha;">
<li>10%</li>
<li>50%</li>
<li>70%</li>
<li>90%</li>
</ol>
<p> </p>
Probabilityhttp://gateoverflow.in/46592/cmi2013-a-02Mon, 23 May 2016 13:28:36 +0000Conditional Probability IITB (RA) 2016
http://gateoverflow.in/46150/conditional-probability-iitb-ra-2016
This question was asked in IITB (RA) admissions 2016.<br />
<br />
I have two blue dice, with which I play a game. If I throw a double six (i.e. if I get two six on both the dices) then I win the game. I separately throw a red dice. If I get a one, then I tell truth about whether I win/loose in the previous game, otherwise I lie. I just rolled the three die. I turn around to you and said, "I won!". What is the probability that I actually won the game?Probabilityhttp://gateoverflow.in/46150/conditional-probability-iitb-ra-2016Thu, 19 May 2016 07:03:30 +0000ISRO-2013-71
http://gateoverflow.in/45660/isro-2013-71
<p>Let $P(E)$ denote the probability of the occurrence of event $E$. If $P(A)= 0.5$ and $P(B)=1$ then the values of $P(A|B)$ and $P(B|A)$ respectively are</p>
<ol style="list-style-type: upper-alpha;">
<li>$0.5, 0.25$</li>
<li>$0.25, 0.5$</li>
<li>$0.5, 1$</li>
<li>$1, 0.5$</li>
</ol>
Probabilityhttp://gateoverflow.in/45660/isro-2013-71Fri, 13 May 2016 15:36:54 +0000GATE2014-AG-GA10
http://gateoverflow.in/41674/gate2014-ag-ga10
$10$% of the population in a town is HIV$^{+}$. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV$^{+}$ individuals $95$% of the time, and HIV$^{-}$ individuals $89$% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is ______.Numerical Abilityhttp://gateoverflow.in/41674/gate2014-ag-ga10Mon, 21 Mar 2016 19:28:27 +0000GATE2014-EC01-GA10
http://gateoverflow.in/41499/gate2014-ec01-ga10
<p>You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is</p>
<ol style="list-style-type:upper-alpha">
<li>$1/4$ </li>
<li>$1/3$ </li>
<li>$1/2$ </li>
<li>$2/3$ </li>
</ol>Probabilityhttp://gateoverflow.in/41499/gate2014-ec01-ga10Fri, 18 Mar 2016 12:44:46 +0000GATE 2015 Aptitude Set 4 Q10
http://gateoverflow.in/40174/gate-2015-aptitude-set-4-q10
<p>A coin is tossed thrice. Let <em>X </em>be the event that head occurs in each of the first two tosses. Let <em>Y </em>be the event that a tail occurs on the third toss. Let <em>Z </em>be the event that two tails occur in three tosses.
<br>
Based on the above information, which one of the following statements is TRUE?</p>
<p>(A) <em>X </em>and <em>Y </em>are not independent (B) <em>Y </em>and <em>Z </em>are dependent
<br>
(C) <em>Y </em>and <em>Z </em>are independent (D) <em>X </em>and <em>Z </em>are independent
<br>
</p>Numerical Abilityhttp://gateoverflow.in/40174/gate-2015-aptitude-set-4-q10Mon, 15 Feb 2016 14:32:44 +0000GATE 2016-2-05
http://gateoverflow.in/39541/gate-2016-2-05
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.Probabilityhttp://gateoverflow.in/39541/gate-2016-2-05Fri, 12 Feb 2016 11:33:53 +0000GATE 2014 EC
http://gateoverflow.in/38256/gate-2014-ec
<p> </p>
<p><span style="font-family: ;font-size:11pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;">Q.10 You are given three coins: one has heads on both faces, the second has tails on both faces, and the
<br><span style="font-family: ;font-size:11pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;">third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it
<br><span style="font-family: ;font-size:11pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;">comes up heads. The probability that the other face is tails is
<br><span style="font-family: ;font-size:11pt;color:rgb(0,0,0);font-style:normal;font-variant:normal;">(A) 1/4 (B) 1/3 (C) 1/2 (D) 2/3</span></span></span></span>
<br>
</p>
<p>In this question they have given answer (B) as 1/3. We can get B if we take</p>
<p>P(C1) = 1/3, P(C2) = 1/3,P(C3) = 1/3</p>
<p>Where C1 has both head / tail & C2 has Head/Head, C3 has tail/tail.</p>
<p>Issue is that if we know that we have got heads , we can actually eliminate P(C3) , we can take it as 0.</p>
<p>Because it is given that we get Head when we toss it. (C3 can't generate head)</p>
<p>If we consider P(C1) = 1/2, P(C2) = 1/2 & P(C3) = 0 then answer I get is (D) 2/3 which is wrong as per GATE key. So please answer the question & Also let me know why should we consider C3 , if we know surely that coin is not C3.</p>
Numerical Abilityhttp://gateoverflow.in/38256/gate-2014-ecThu, 28 Jan 2016 14:21:03 +0000TIFR-2011-Maths-B-10
http://gateoverflow.in/30288/tifr-2011-maths-b-10
Suppose a box contains three cards, one with both sides white, one with both sides black, and one with one side white and the other side black. If you pick a card at random, and the side facing you is white, then the probability that the other side is white is $1/2$.Probabilityhttp://gateoverflow.in/30288/tifr-2011-maths-b-10Thu, 10 Dec 2015 10:19:05 +0000Conditional Probability
http://gateoverflow.in/26475/conditional-probability
A die is thrown 3 times and sum of 3 numbers thrown is 15. Find the chance that first thrown is 4 ?Probabilityhttp://gateoverflow.in/26475/conditional-probabilitySat, 14 Nov 2015 23:07:38 +0000random variables
http://gateoverflow.in/25174/random-variables
Consider two independent random variables X and Y with identical distributions.The variables X and Y take blue 0, 1 and 2 with probabilities 1/2, 1/4 and 1/4 respectively. What is conditional probability P(X+Y=2/X-Y=0)???Probabilityhttp://gateoverflow.in/25174/random-variablesMon, 02 Nov 2015 11:34:51 +0000TIFR2012-A-1
http://gateoverflow.in/20938/tifr2012-a-1
<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, "Amar told me that India won". What probability should Anthony assign to India's win?</p>
<ol style="list-style-type: lower-alpha;">
<li>$9 / 16$</li>
<li>$6 / 16$</li>
<li>$7 / 16$</li>
<li>$10 / 16$</li>
<li>None of the above.</li> </ol>Probabilityhttp://gateoverflow.in/20938/tifr2012-a-1Sun, 25 Oct 2015 18:45:32 +0000TIFR2010-A-19, TIFR2014-A-6
http://gateoverflow.in/18499/tifr2010-a-19-tifr2014-a-6
<p>Karan tells truth with probability 1/3 and lies with probability 2/3. Independently, Arjun tells truth with probability 3/4 and lies with probability 1/4. Both watch a cricket match. Arjun tells you that India won, Karan tells you that India lost. What probability will you assign to India's win?</p>
<ol style="list-style-type:lower-alpha">
<li>1/2</li>
<li>2/3</li>
<li>3/4</li>
<li>5/6</li>
<li>6/7</li>
</ol>Probabilityhttp://gateoverflow.in/18499/tifr2010-a-19-tifr2014-a-6Sun, 04 Oct 2015 19:37:55 +0000probability
http://gateoverflow.in/16432/probability
Let x be the number obtained from rolling a fair dice and you toss an unbiassed coin X times. What is the probablity that X=5 given that you have obtained 3 heads from X tosses?Probabilityhttp://gateoverflow.in/16432/probabilityWed, 09 Sep 2015 17:19:13 +0000GATE1994-1.4, ISRO2017-2
http://gateoverflow.in/2441/gate1994-1-4-isro2017-2
<p>Let A and B be any two arbitrary events, then, which one of the following is true?</p>
<ol style="list-style-type:upper-alpha">
<li>
<p>$P (A \cap B) = P(A)P(B)$</p>
</li>
<li>
<p>$P (A \cup B) = P(A)+P(B)$</p>
</li>
<li>
<p>$P (A \mid B) = P(A \cap B)P(B)$</p>
</li>
<li>
<p>$P (A \cup B) \leq P(A) + P(B)$</p>
</li>
</ol>
<p> </p>Probabilityhttp://gateoverflow.in/2441/gate1994-1-4-isro2017-2Sat, 04 Oct 2014 11:17:31 +0000GATE2012_33
http://gateoverflow.in/1751/gate2012_33
<p>Suppose 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. What is the probability that the sum total of values that turn up is at least 6?</p>
<ol style="list-style-type: upper-alpha;">
<li>$10/21$</li>
<li>$5/12$</li>
<li>$2/3$</li>
<li>$1/6$</li>
</ol>
Probabilityhttp://gateoverflow.in/1751/gate2012_33Fri, 26 Sep 2014 13:45:29 +0000GATE2005-51
http://gateoverflow.in/1176/gate2005-51
<p>Box P has 2 red balls and 3 blue balls and box Q has 3 red balls and 1 blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes P and Q are 1/3 and 2/3 respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box P is:</p>
<ol style="list-style-type: upper-alpha;">
<li>4/19</li>
<li>5/19</li>
<li>2/9</li>
<li>19/30</li>
</ol>Probabilityhttp://gateoverflow.in/1176/gate2005-51Sun, 21 Sep 2014 12:00:16 +0000