GATE Overflow for GATE CSE - Recent questions tagged conditional-probability
https://gateoverflow.in/tag/conditional-probability
Powered by Question2AnswerConditional Probability
https://gateoverflow.in/389295/conditional-probability
English and American spelling are rigour and rigor, respectively. A man staying at Al Rashid hotel writes this word, and a letter taken at random from his spelling is found to be a vowel. If 40 percent of the English-speaking men at the hotel are English and 60 percent are American, what is the probability that the writer is an Englishman?Probabilityhttps://gateoverflow.in/389295/conditional-probabilityThu, 24 Nov 2022 15:42:45 +0000TIFR CS & SS 2018 SS part Question 12
https://gateoverflow.in/389114/tifr-cs-%26-ss-2018-ss-part-question-12
Suppose that Amitabh Bachchan has ten coins in his pocket. 3 coins have tails on both sides. 4 coins have heads on both sides. 3 coins have heads on one side and tails on the other and both the outcomes are equally likely when that coin is flipped. In a bet with Dharmendra, Amitabh picks up a coin at random (each coin is equally likely to be picked) from these ten coins, flips it and finds that the outcome is tails. What is the probability that the other side of this coin is heads?Probabilityhttps://gateoverflow.in/389114/tifr-cs-%26-ss-2018-ss-part-question-12Tue, 22 Nov 2022 09:46:36 +0000A First Course In Probability, 9th Edition, Indian Version, Sheldon Ross, Chapter 3, Problems, 33.
https://gateoverflow.in/382652/course-probability-edition-version-sheldon-chapter-problems
The meteorology department predicts the rain correctly with a probability of 4/5. When rain is predicted Amit travels by his car. When rain is not forecasted, he travels with his car with a probability of 0.5. Assuming that it rains in a day with a probability of 1/2. Find the probability that Amit does not travel by car given it rains.Probabilityhttps://gateoverflow.in/382652/course-probability-edition-version-sheldon-chapter-problemsSat, 10 Sep 2022 06:15:08 +0000TIFR CSE 2022 | Part A | Question: 10
https://gateoverflow.in/381942/tifr-cse-2022-part-a-question-10
<p>Consider a bag containing colored marbles. There are $n$ marbles in the bag such that there is exactly one pair of marbles of color $i$ for each $i \in\{1, \ldots, m\}$ and the rest of the marbles are of distinct colors (different from colors $\{1, \ldots, m\}$ ). You draw two marbles uniformly at random (without replacement). What is the probability that both marbles are of same color?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\frac{m}{n}$</li>
<li>$\frac{2m}{n}$</li>
<li>$\frac{2m}{n(n-1)}$</li>
<li>$\frac{2m}{n^2}$</li>
<li>$\frac{m}{n(n-1)}$</li>
</ol>Probabilityhttps://gateoverflow.in/381942/tifr-cse-2022-part-a-question-10Thu, 01 Sep 2022 01:29:12 +0000TIFR CSE 2022 | Part A | Question: 12
https://gateoverflow.in/381940/tifr-cse-2022-part-a-question-12
<p>Alice plays the following game on a math show. There are $7$ boxes and identical prizes are hidden inside $3$ of the boxes. Alice is asked to choose a box where a prize might be. She chooses a box uniformly at random. From the unchosen boxes which do not have a prize, the host opens an arbitrary box and shows Alice that there is no prize in it. The host then allows Alice to change her choice if she so wishes. Alice chooses a box uniformly at random from the other $5$ boxes (other than the one she chose first and the one opened by the host). Her probability of winning the prize is</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$3 / 7$</li>
<li>$1 / 2$</li>
<li>$17 / 30$</li>
<li>$18 / 35$</li>
<li>$9 / 19$</li>
</ol>Probabilityhttps://gateoverflow.in/381940/tifr-cse-2022-part-a-question-12Thu, 01 Sep 2022 01:29:12 +0000Best Open Video Playlist for Conditional Probability Topic | Quantitative Aptitude
https://gateoverflow.in/381464/playlist-conditional-probability-quantitative-aptitude
<p>Please list out the best free available video playlist for Conditional Probability from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to <a href="http://classroom.gateoverflow.in" rel="nofollow">GO classroom</a> video lists. You can add any video playlist link including your own (as long as they are free to access) but standard ones are more likely to be selected as best.<br>
<br>
For the full list of selected videos please see <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQTEfCg28q1B_buKRxaVvUjN_CTu9UntAiqi9qBiZZesmJE6LnqfkuwxNQOsNcU1g/pubhtml" rel="nofollow">here</a></p>Study Resourceshttps://gateoverflow.in/381464/playlist-conditional-probability-quantitative-aptitudeThu, 25 Aug 2022 14:44:10 +0000Best Open Video Playlist for Conditional Probability Topic | Probability
https://gateoverflow.in/380544/video-playlist-conditional-probability-topic-probability
<p>Please list out the best free available video playlist for <strong>Conditional Probability</strong> Topic from Probability as an answer here (only one playlist per answer). We'll then select the best playlist and add to <a href="http://classroom.gateoverflow.in" rel="nofollow">GO classroom</a> video lists. You can add any video playlist link including your own (as long as they are free to access) but standard ones are more likely to be selected as best.<br>
<br>
For the full list of selected videos please see <a href="https://docs.google.com/spreadsheets/d/e/2PACX-1vQTEfCg28q1B_buKRxaVvUjN_CTu9UntAiqi9qBiZZesmJE6LnqfkuwxNQOsNcU1g/pubhtml" rel="nofollow">here</a></p>Study Resourceshttps://gateoverflow.in/380544/video-playlist-conditional-probability-topic-probabilityMon, 15 Aug 2022 11:16:53 +0000Probability
https://gateoverflow.in/371262/probability
<ol>
<li>A survey was conducted with recent MBAs of two different universities about their annual incomes. The following table displays data collected.</li>
</ol>
<table border="1">
<tbody>
<tr>
<td style="vertical-align:top; width:110.4pt">
<p>Annual Income</p>
</td>
<td style="vertical-align:top; width:111.3pt">
<p>University X</p>
</td>
<td style="vertical-align:top; width:111.35pt">
<p>University Y</p>
</td>
<td style="vertical-align:top; width:109.75pt">
<p>Total</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:110.4pt">
<p>Under 8L</p>
</td>
<td style="vertical-align:top; width:111.3pt">
<p>36</p>
</td>
<td style="vertical-align:top; width:111.35pt">
<p>24</p>
</td>
<td style="vertical-align:top; width:109.75pt">
<p>60</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:110.4pt">
<p>8L to 12L</p>
</td>
<td style="vertical-align:top; width:111.3pt">
<p>109</p>
</td>
<td style="vertical-align:top; width:111.35pt">
<p>56</p>
</td>
<td style="vertical-align:top; width:109.75pt">
<p>165</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:110.4pt">
<p>12L and above</p>
</td>
<td style="vertical-align:top; width:111.3pt">
<p>35</p>
</td>
<td style="vertical-align:top; width:111.35pt">
<p>40</p>
</td>
<td style="vertical-align:top; width:109.75pt">
<p>75</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:110.4pt">
<p>Total</p>
</td>
<td style="vertical-align:top; width:111.3pt">
<p>180</p>
</td>
<td style="vertical-align:top; width:111.35pt">
<p>120</p>
</td>
<td style="vertical-align:top; width:109.75pt">
<p>300</p>
</td>
</tr>
</tbody>
</table>
<p>Answer following questions using the table above</p>
<ol style="list-style-type:lower-alpha">
<li>What is the probability that a student is from University X if their salary is more than 12L?</li>
<li>What is the probability that an MBA gets salary less than 8L?</li>
<li>What is the probability that an MBA from university Y earns 10L annually?</li>
</ol>Probabilityhttps://gateoverflow.in/371262/probabilityTue, 08 Feb 2022 20:55:19 +0000Probability
https://gateoverflow.in/371261/probability
<ol>
<li>Use the following data.</li>
</ol>
<table border="1">
<tbody>
<tr>
<td style="vertical-align:top; width:108.75pt">
<p> </p>
</td>
<td style="vertical-align:top; width:105.75pt">
<p>Have pets</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>Do not have pets</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>Total</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:108.75pt">
<p>Men</p>
</td>
<td style="vertical-align:top; width:105.75pt">
<p>0.41</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>0.08</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>0.49</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:108.75pt">
<p>Women</p>
</td>
<td style="vertical-align:top; width:105.75pt">
<p>0.45</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>0.06</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>0.51</p>
</td>
</tr>
<tr>
<td style="vertical-align:top; width:108.75pt">
<p>Total</p>
</td>
<td style="vertical-align:top; width:105.75pt">
<p>0.86</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>0.14</p>
</td>
<td style="vertical-align:top; width:105.8pt">
<p>1</p>
</td>
</tr>
</tbody>
</table>
<ol style="list-style-type:lower-alpha">
<li>What is the probability of a randomly selected person being a man, given that they do not own a pet?</li>
<li>What is the probability for a woman to be a pet owner?</li>
<li>How likely is that a randomly selected person is a pet owner man?</li>
</ol>Probabilityhttps://gateoverflow.in/371261/probabilityTue, 08 Feb 2022 20:54:44 +0000Conditional Probability
https://gateoverflow.in/368275/conditional-probability
<p style="text-align:center"><img alt="Conditional Probability" height="260" src="https://gateoverflow.in/?qa=blob&qa_blobid=15763123621577054698" width="450"></p>
<p>The above-given problem is from MIT-OCW probability – <a href="https://tinyurl.com/25wamnxz" rel="nofollow">https://tinyurl.com/25wamnxz</a></p>
<p> </p>
<p><strong>There are two biased coins – A and B. The probability of choosing either coin is 0.5. Once the coins are chosen, we perform the experiment of tossing the coins as shown in the figure above. The probabilities for heads and tails for respective coins are given below:</strong></p>
<p><strong>Coin A –</strong></p>
<p><strong> Probability of Head: 0.9</strong></p>
<p><strong> Probability of Tail: 0.1</strong></p>
<p><strong>Coin B –</strong></p>
<p><strong> Probability of Head: 0.1</strong></p>
<p><strong> Probability of Tail: 0.9</strong></p>
<p> </p>
<p>************************************************************************************************</p>
<p> </p>
<p><em><strong>Event A: Coin A is chosen</strong></em></p>
<p><em><strong>Event B: first 10 tosses are heads</strong></em></p>
<h3>What is the probability of <em><strong>(A | B)</strong></em> i.e. <strong>if we get 10 successive heads, then what is the probability that coin A was chosen?</strong></h3>Probabilityhttps://gateoverflow.in/368275/conditional-probabilitySun, 26 Dec 2021 06:49:34 +0000GATE Mechanical 2021 Set 2 | GA Question: 7
https://gateoverflow.in/359497/gate-mechanical-2021-set-2-ga-question-7
<p>A box contains $15$ blue balls and $45$ black balls. If $2$ balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____</p>
<ol style="list-style-type:upper-alpha" type="A">
<li>$\frac{3}{16}$</li>
</ol>
<ol start="2" style="list-style-type:upper-alpha" type="A">
<li>$\frac{45}{236}$</li>
</ol>
<ol start="100" style="list-style-type:upper-roman" type="I">
<li>$\frac{1}{4}$</li>
</ol>
<ol start="500" style="list-style-type:upper-roman" type="I">
<li>$\frac{3}{4}$</li>
</ol>Quantitative Aptitudehttps://gateoverflow.in/359497/gate-mechanical-2021-set-2-ga-question-7Mon, 01 Mar 2021 01:08:34 +0000GATE CSE 2021 Set 1 | Question: 54
https://gateoverflow.in/357396/gate-cse-2021-set-1-question-54
<p>A sender $(\textsf{S})$ transmits a signal, which can be one of the two kinds: $H$ and $L$ with probabilities $0.1$ and $0.9$ respectively, to a receiver $(\textsf{R})$.</p>
<p>In the graph below, the weight of edge $(u,v)$ is the probability of receiving $v$ when $u$ is transmitted, where $u,v \in \{H,L\}$. For example, the probability that the received signal is $L$ given the transmitted signal was $H$, is $0.7$.</p>
<p style="text-align:center"><img alt="" height="173" src="https://gateoverflow.in/?qa=blob&qa_blobid=7079308523429416349" width="275"></p>
<p>If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.</p>Probabilityhttps://gateoverflow.in/357396/gate-cse-2021-set-1-question-54Thu, 18 Feb 2021 08:49:07 +0000CMI-2018-DataScience-A: 12
https://gateoverflow.in/355864/cmi-2018-datascience-a-12
In an entrance examination with multiple choice questions, with each question having four options and a single correct answer, suppose that only $20\%$ candidates think they know the answer to one difficult question and only half of them know it correctly and the other half get it wrong. The remaining candidates pick one option out of the four randomly and tick the same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?Othershttps://gateoverflow.in/355864/cmi-2018-datascience-a-12Fri, 29 Jan 2021 10:29:22 +0000NIELIT Scientific Assistant A 2020 November: 99
https://gateoverflow.in/351361/nielit-scientific-assistant-a-2020-november-99
<p>A bag contains $10$ white balls and $5$ blue balls. A ball is drawn from the bag and its color is noted. This ball is put back in the bag along with $3$ more balls of the same color. A ball is drawn again from the bag at random. The probability that the first ball drawn is blue, given that the second ball drawn is blue, is:</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$1/3$</li>
<li>$3/4$</li>
<li>$8/9$</li>
<li>$4/9$</li>
</ol>Probabilityhttps://gateoverflow.in/351361/nielit-scientific-assistant-a-2020-november-99Wed, 09 Dec 2020 07:18:49 +0000TIFR CSE 2020 | Part A | Question: 11
https://gateoverflow.in/333113/tifr-cse-2020-part-a-question-11
<p>Suppose we toss $m=3$ labelled balls into $n=3$ numbered bins. Let $A$ be the event that the first bin is empty while $B$ be the event that the second bin is empty. $P(A)$ and $P(B)$ denote their respective probabilities. Which of the following is true?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$P(A)>P(B)$</li>
<li>$P(A) = \dfrac{1}{27}$</li>
<li>$P(A)>P(A\mid B)$</li>
<li>$P(A)<P(A\mid B)$</li>
<li>None of the above</li>
</ol>Probabilityhttps://gateoverflow.in/333113/tifr-cse-2020-part-a-question-11Mon, 10 Feb 2020 18:35:36 +0000CMI2018-A-6
https://gateoverflow.in/320487/cmi2018-a-6
<p>You are given two coins $A$ and $B$ that look identical. The probability that coin $A$ turns up heads is $\frac{1}{4}$, while the probability that coin $B$ turns up heads is $\frac{3}{4}.$ You choose one of the coins at random and toss it twice. If both the outcomes are heads, what is the probability that you chose coin $B?$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\frac{1}{16}$</li>
<li>$\frac{1}{2}$</li>
<li>$\frac{9}{16}$</li>
<li>$\frac{9}{10}$</li>
</ol>Probabilityhttps://gateoverflow.in/320487/cmi2018-a-6Fri, 13 Sep 2019 14:34:31 +0000CMI2018-A-7
https://gateoverflow.in/320486/cmi2018-a-7
<p>Let $C_{n}$ be the number of strings $w$ consisting of $n$ $X's$ and $n$ $Y's$ such that no initial segment of $w$ has more $Y's$ than $X's.$ Now consider the following problem. A person stands on the edge of a swimming pool holding a bag of $n$ red and $n$ blue balls. He draws a ball out one at a time and discards it. If he draws a blue ball, he takes one step back, if he draws a red ball, he moves one step forward. What is the probability that the person remains dry?</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>$\frac{C_{n}}{2^{2n}}$</li>
<li>$\frac{C_{n}}{\binom{2n}{n}}$</li>
<li>$\frac{n\cdot C_{n}}{(2n)!}$</li>
<li>$\frac{n\cdot C_{n}}{\binom{2n}{n}}$</li>
</ol>Probabilityhttps://gateoverflow.in/320486/cmi2018-a-7Fri, 13 Sep 2019 14:34:30 +0000CMI2018-A-8
https://gateoverflow.in/320485/cmi2018-a-8
<p>There are $7$ switches on a switchboard, some of which are on and some of which are off. In one move, you pick any $2$ switches and toggle each of them-if the switch you pick is currently off, you turn it on, if it is on, you turn it off. Your aim is to execute a sequence of moves and turn all $7$ switches on. For which of the following initial configurations is this not possible? Each configuration lists the initial positions of the $7$ switches in sequence, from switch $1$ to switch $7.$</p>
<ol start="1" style="list-style-type:upper-alpha">
<li>(off,on,off,on,off,off,on)</li>
<li>(off,on,on,on,on,on,off)</li>
<li>(on,off,on,on,on,on,on)</li>
<li>(off,off,off,off,off,on,off)</li>
</ol>Probabilityhttps://gateoverflow.in/320485/cmi2018-a-8Fri, 13 Sep 2019 14:34:30 +0000Conditional Probability
https://gateoverflow.in/304357/conditional-probability
A multiple choice exam has 4 choices for each question. A student has studied enough so that the probability they will know the answer to a question is 0.5, the probability that they will be able to eliminate one choice is 0.25, otherwise all 4 choices seem equally plausible. If they know the answer they will get the question right. If not they have to guess from the 3 or 4 choices.<br />
<br />
As the teacher you want the test to measure what the student knows. If the student answers a question correctly what’s the probability they knew the answer?Probabilityhttps://gateoverflow.in/304357/conditional-probabilityMon, 18 Feb 2019 05:29:28 +0000Conditional probability
https://gateoverflow.in/304248/conditional-probability
Oscar has lost his dog in either forest A (with a priori probability 0.4) or in forest B (with a priori probability 0.6). On any given day, if the dog is in A and Oscar spends a day searching for it in A, the conditional probability that he will ﬁnd the dog that day is 0.25. Similarly, if the dog is in B and Oscar spends a day looking for it there, the conditional probability that he will ﬁnd the dog that day is 0.15. The dog cannot go from one forest to the other. Oscar can search only in the daytime, and he can travel from one forest to the other only at night. <br />
<br />
<br />
Q> If Oscar ﬂips a fair coin to determine where to look on the ﬁrst day and ﬁnds the dog on the ﬁrst day, what is the probability that he looked in A?<br />
<br />
According to me P(finding the dog)=(1/2)*0.25+(1/2)*0.15;<br />
<br />
but the answer given is=(0.5*0.4*0.25)+(0.5*0.6*0.15); <br />
<br />
what is wrong with my logic?Probabilityhttps://gateoverflow.in/304248/conditional-probabilitySat, 16 Feb 2019 13:42:24 +0000Applied Course Mock Test 4
https://gateoverflow.in/298441/applied-course-mock-test-4
<p>Q32 [Mock 4]. Naveen's coin box contains 8 fair standard coins (heads and tails) and 1 coin which has heads on both sides. He selects a coin randomly and flips it 4 times, getting all heads. If he flips this coin again, what is the probability it will be heads?</p>
<ol style="list-style-type:upper-alpha" type="A">
<li>1/3</li>
</ol>
<ol start="2" style="list-style-type:upper-alpha" type="A">
<li>2/3</li>
</ol>
<ol start="100" style="list-style-type:upper-roman" type="I">
<li>1/6</li>
</ol>
<ol start="500" style="list-style-type:upper-roman" type="I">
<li><strong>5/6</strong></li>
</ol>
<p> </p>
<p><strong>They’ve used Bayes theorem to solve this question. But I feel the concept of conditional probability is not applicable here. Because the question asks for the outcome on </strong><strong>fifth</strong><strong> flip only and assumes that the initial four flips have already happened. </strong></p>
<p>References for their solution:<a rel="nofollow" href="https://docs.google.com/document/d/1zIwY4lm8oCzWo9q57jAmB0dNXZmTrd3VsFX4nwsNuJE/edit">https://docs.google.com/document/d/1zIwY4lm8oCzWo9q57jAmB0dNXZmTrd3VsFX4nwsNuJE/</a></p>
<p> </p>
<p> </p>
<p>I feel the answer should be (8/9)*(1/2)+(1/9)*(1)</p>
<p>Probability of choosing fair coin and P(heads)+ P(unfair)*P(heads).</p>
<p>Please help me understand this question.</p>
<p> </p>
<p> </p>Probabilityhttps://gateoverflow.in/298441/applied-course-mock-test-4Tue, 22 Jan 2019 12:30:27 +0000probability
https://gateoverflow.in/297745/probability
Probability density function of a random variable X is distributed uniformly between 0 and 10 The probability that X lies between 2.5 to 7.5 and the mean square value of X are respectively.<br />
<br />
please give step by step answer in a detailed manner.Probabilityhttps://gateoverflow.in/297745/probabilityMon, 21 Jan 2019 02:46:29 +0000probability
https://gateoverflow.in/297401/probability
In a lottery, 10 tickets are drawn at random out of 50 tickets numbered from 1 to 50. What is the expected value of the sum of numbers on the drawn tickets?Mathematical Logichttps://gateoverflow.in/297401/probabilitySun, 20 Jan 2019 13:03:32 +0000probability
https://gateoverflow.in/297282/probability
<p>A <em>player tosses two fair coins</em>. <em>He wins rs 2 if 2 heads occur</em> and <em>rs 1 if 1 head occurs</em>. On the <em>other hand</em>, <em>he</em> loses <em>rs</em> 3 <em>if</em> no <em>heads occur. if the player plays 100 times.then the amount he wins______________(RS).</em></p>Mathematical Logichttps://gateoverflow.in/297282/probabilitySun, 20 Jan 2019 08:34:44 +0000Probability
https://gateoverflow.in/296790/probability
<p><strong>Prabha is working in a software company. Her manager is running a dinner for those employees having atleast one son. If Prabha is invited to the dinner and everyone knows she has two children. What is the probability that they are both boys? </strong></p>Mathematical Logichttps://gateoverflow.in/296790/probabilitySat, 19 Jan 2019 08:56:56 +0000GATE Overflow | Mock GATE | Test 1 | Question: 42
https://gateoverflow.in/285437/gate-overflow-mock-gate-test-1-question-42
<p>An urn contains $m$ WHITE and $n$ BLACK balls. A ball is drawn at random and is put back into the urn along with $k$ additional balls of the same color as that of the ball drawn. If now a ball is drawn, the probability that it is WHITE is?</p>
<ol style="list-style-type:upper-alpha">
<li>$(m+k)/(m+n+k)$</li>
<li>$(n+k)/(m+n+k)$</li>
<li>$m/(m+n+k)$</li>
<li>$m/(m+n)$</li>
</ol>Probabilityhttps://gateoverflow.in/285437/gate-overflow-mock-gate-test-1-question-42Thu, 27 Dec 2018 17:24:48 +0000