GATE Overflow - Recent questions tagged conditional-probability
http://gateoverflow.in/tag/conditional-probability
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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 07:51:58 +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-probabilitySat, 06 Aug 2016 23:36:03 +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-probabilitySat, 06 Aug 2016 23:15:52 +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 01:45:42 +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 07:58:36 +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 01:33:30 +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 10:06:54 +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 13:58:27 +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 07:14:46 +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 09:02:44 +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 06:03:53 +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 08:51:03 +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 04:49:05 +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 17:37:38 +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 06:04:51 +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 13:15:32 +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 14:07:55 +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 11:49:13 +0000GATE1994_1.4
http://gateoverflow.in/2441/gate1994_1-4
<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_1-4Sat, 04 Oct 2014 05:47:31 +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 08:15:29 +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 06:30:16 +0000