Recent questions tagged conditional-probability / GATE Overflow for GATE CSE

3 votes

1 answer

91

GATE Overflow Test Series | Mock GATE | Test 6 | Question: 2
The probability that it is Monday and a student is absent is $0.08.$ Assuming there are $5$ school days in a week, what is the probability that a student is absent given that today is Monday?

The probability that it is Monday and a student is absent is $0.08.$ Assuming there are $5$ school days in a week, what is the probability that a student is absent given ...

Arjun

172 views

Arjun asked Jan 30, 2022

2 votes

1 answer

92

GATE Overflow Test Series | Mock GATE | Test 6 | Question: 26
A fair die is thrown as long as necessary for $6$ to turn up. If the number of throws $(n)$ turns out to be odd, the probability that $n=5$ is ________ (rounded to $2$ decimal points)

A fair die is thrown as long as necessary for $6$ to turn up. If the number of throws $(n)$ turns out to be odd, the probability that $n=5$ is ________ (rounded to $2$ de...

Arjun

217 views

Arjun asked Jan 30, 2022

0 votes

1 answer

93

Conditional Probability
The above-given problem is from MIT-OCW probability - https://tinyurl.com/25wamnxz 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 ... probability of (A | B) i.e. if we get 10 successive heads, then what is the probability that coin A was chosen?

The above-given problem is from MIT-OCW probability – https://tinyurl.com/25wamnxz There are two biased coins – A and B. The probability of choosing either coin is 0...

allSystemsDown

560 views

allSystemsDown asked Dec 26, 2021

3 votes

1 answer

94

GATE Mechanical 2021 Set 2 | GA Question: 7
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 _____ $\frac{3}{16}$ $\frac{45}{236}$ $\frac{1}{4}$ $\frac{3}{4}$

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...

go_editor

1.7k views

go_editor asked Mar 1, 2021

21 votes

2 answers

95

GATE CSE 2021 Set 1 | Question: 54
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 $(\textsf{R})$. In the graph below, the weight of edge $(u,v)$ is the ... $0.7$. If the received signal is $H,$ the probability that the transmitted signal was $H$ (rounded to $2$ decimal places) is __________.

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 $(\textsf{R})$.I...

Arjun

5.6k views

Arjun asked Feb 18, 2021

9 votes

1 answer

96

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 64
In the city of Rebuke birth rate is uniform for all months except September where the number of births is double the normal. Also, $3$ girl children are born in September for every $2$ boy children where as the ratio is the ... gender) is born in Rebuke what is the probability that her birthday is in September? (up to $3$ decimal places)

In the city of Rebuke birth rate is uniform for all months except September where the number of births is double the normal. Also, $3$ girl children are born in September...

gatecse

627 views

gatecse asked Feb 8, 2021

3 votes

1 answer

97

GATE Overflow Test Series | Mock GATE | Test 4 | Question: 51
A fair die is thrown as long as necessary for $6$ to turn up. If the number of throws $(n)$ turns out to be odd, the probability that $n=5$ is ______ (rounded to three decimal places)

A fair die is thrown as long as necessary for $6$ to turn up. If the number of throws $(n)$ turns out to be odd, the probability that $n=5$ is ______ (rounded to three de...

gatecse

505 views

gatecse asked Feb 1, 2021

0 votes

2 answers

98

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 ... same. If a candidate has correctly answered the question, what is the (conditional) probability that she knew the answer?

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 t...

soujanyareddy13

911 views

soujanyareddy13 asked Jan 29, 2021

5 votes

1 answer

99

GATE Overflow Test Series | Mock GATE | Test 3 | Question: 61
Two coins are in a box. The coins look alike, but one coin is fair (with equal probabilities for Head and Tail), while the other coin is biased, with $2/3$ probability of Heads. One of the coins is randomly chosen from the hat, without knowing which ... chosen coin is the fair coin? $\dfrac{4}{5}$ $0.692$ $\dfrac{9}{25}$ $\dfrac{1}{2}$

Two coins are in a box. The coins look alike, but one coin is fair (with equal probabilities for Head and Tail), while the other coin is biased, with $2/3$ probability of...

gatecse

271 views

gatecse asked Jan 26, 2021

3 votes

1 answer

100

GATE Overflow Test Series | Mock GATE | Test 2 | Question: 5
A deck of $9$ cards numbered $1$ through $9$ is shuffled, and a card is drawn from the deck. If a card is drawn and the number is even, what is the probability that the number is prime? $\dfrac{1}{5}$ $\dfrac{1}{6}$ $\dfrac{2}{7}$ $\dfrac{1}{4}$

A deck of $9$ cards numbered $1$ through $9$ is shuffled, and a card is drawn from the deck. If a card is drawn and the number is even, what is the probability that the n...

gatecse

175 views

gatecse asked Jan 17, 2021

5 votes

1 answer

101

GATE Overflow Test Series | Mock GATE | Test 1 | Question: 58
A school has three divisions-- $A,B$ and $C$ for the tenth grade, having the number of students $40, 45$ and $42$ respectively. The pass percentages of students from the three divisions are $96, 97$ and $98$ respectively. If a ... in the exam, what is the probability that it he/she is from the $A$ grade? (Rounded to $2$ decimal points)

A school has three divisions $A,B$ and $C$ for the tenth grade, having the number of students $40, 45$ and $42$ respectively. The pass percentages of students from the t...

gatecse

571 views

gatecse asked Jan 3, 2021

2 votes

1 answer

102

NIELIT Scientific Assistant A 2020 November: 99
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: $1/3$ $3/4$ $8/9$ $4/9$

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...

gatecse

761 views

gatecse asked Dec 9, 2020

2 votes

2 answers

103

GATE Overflow Test Series | Probability | Test 1 | Question: 19
In a car factory wings $A,B,C$ manufacture $30, 33$ and $37$ percent of the total engines, respectively. Of their output $4, 3$ and $2$ percent respectively are defective. If an engine is drawn at random from the ... is found defective, what is the probability that it was manufactured in the $C$ wing? (Rounded to $2$ decimal points)

In a car factory wings $A,B,C$ manufacture $30, 33$ and $37$ percent of the total engines, respectively. Of their output $4, 3$ and $2$ percent respectively are defective...

gatecse

145 views

gatecse asked Sep 22, 2020

1 votes

2 answers

104

GATE Overflow Test Series | Probability | Test 1 | Question: 22
Die A has three red and three green faces, whereas die B has four red and two green faces. A fair coin is flipped once. If it falls head, die A is chosen and if it falls tail die B is chosen. The chosen die is thrown repeatedly. If the first $4$ throws turn out to be red, what's the probability that die A is being used?

Die A has three red and three green faces, whereas die B has four red and two green faces. A fair coin is flipped once. If it falls head, die A is chosen and if it falls ...

gatecse

196 views

gatecse asked Sep 22, 2020

5 votes

2 answers

105

GATE Overflow Test Series | Probability | Test 1 | Question: 24
A bag contains one apple which is either green or red, with equal probabilities for both. A green apple is put in the bag (so there are 2 apples now), and then a random apple is taken out. The apple taken out is green. What is the probability that the ... apple is also green? $\frac{2}{3}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{1}{4}$

A bag contains one apple which is either green or red, with equal probabilities for both. A green apple is put in the bag (so there are 2 apples now), and then a random a...

gatecse

288 views

gatecse asked Sep 22, 2020

1 votes

2 answers

106

GATE Overflow Test Series | Probability | Test 1 | Question: 26
Two coins are in a box. The coins look alike, but one coin is fair (with equal probabilities for Head and Tail), while the other coin is biased, with $1/3$ probability of Heads. One of the coins is randomly chosen from the hat, without knowing which ... chosen coin is the fair coin? $\dfrac{4}{5}$ $0.692$ $\dfrac{1}{4}$ $\dfrac{1}{2}$

Two coins are in a box. The coins look alike, but one coin is fair (with equal probabilities for Head and Tail), while the other coin is biased, with $1/3$ probability of...

gatecse

131 views

gatecse asked Sep 22, 2020

6 votes

2 answers

107

GATE Overflow Test Series | Probability | Test 1 | Question: 30
A fair die is thrown as long as necessary for $1$ to turn up. If the number of throws $(n)$ turns out to be even, the probability that $n=4$ is ______ $1/36$ $5/36$ $1/6^4$ None of the above

A fair die is thrown as long as necessary for $1$ to turn up. If the number of throws $(n)$ turns out to be even, the probability that $n=4$ is ______$1/36$$5/36$$1/6^4$N...

gatecse

380 views

gatecse asked Sep 22, 2020

5 votes

1 answer

108

GATE Overflow Test Series | Quantitative Aptitude | Test 1 | Question: 21
The probability that it is Monday and a student is absent is $0.05.$ Since there are $4$ school days in week, the probability that it is Monday is $0.25$. What is the probability that a student is absent given that today is Monday? $16.666\%$ $25\%$ $10\%$ $20\%$

The probability that it is Monday and a student is absent is $0.05.$ Since there are $4$ school days in week, the probability that it is Monday is $0.25$. What is the pro...

gatecse

135 views

gatecse asked Jun 14, 2020

4 votes

1 answer

109

TIFR CSE 2020 | Part A | Question: 11
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? $P(A)>P(B)$ $P(A) = \dfrac{1}{27}$ $P(A)>P(A\mid B)$ $P(A)<P(A\mid B)$ None of the above

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)...

admin

854 views

admin asked Feb 10, 2020

3 votes

2 answers

110

CMI2018-A-6
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 $B?$ $\frac{1}{16}$ $\frac{1}{2}$ $\frac{9}{16}$ $\frac{9}{10}$

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...

gatecse

771 views

gatecse asked Sep 13, 2019

5 votes

2 answers

111

CMI2018-A-7
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 ... $\frac{C_{n}}{\binom{2n}{n}}$ $\frac{n\cdot C_{n}}{(2n)!}$ $\frac{n\cdot C_{n}}{\binom{2n}{n}}$

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 p...

gatecse

600 views

gatecse asked Sep 13, 2019

4 votes

2 answers

112

CMI2018-A-8
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 ... (off,on,off,on,off,off,on) (off,on,on,on,on,on,off) (on,off,on,on,on,on,on) (off,off,off,off,off,on,off)

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 ...

gatecse

1.0k views

gatecse asked Sep 13, 2019

3 votes

1 answer

113

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 ... the test to measure what the student knows. If the student answers a question correctly what's the probability they knew the answer?

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 probabili...

Na462

4.6k views

Na462 asked Feb 18, 2019

1 votes

3 answers

114

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. ... +(1/2)*0.15; but the answer given is=(0.5*0.4*0.25)+(0.5*0.6*0.15); what is wrong with my logic?

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 s...

DIYA BASU

1.9k views

DIYA BASU asked Feb 16, 2019

2 votes

1 answer

115

Applied Course Mock Test 4
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 ... +(1/9)*(1) Probability of choosing fair coin and P(heads)+ P(unfair)*P(heads). Please help me understand this question.

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...

great_gater

1.2k views

great_gater asked Jan 22, 2019

0 votes

0 answers

116

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. please give step by step answer in a detailed manner.

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 ...

learner_geek

588 views

learner_geek asked Jan 21, 2019

2 votes

3 answers

117

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?

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?

learner_geek

3.9k views

learner_geek asked Jan 20, 2019

3 votes

1 answer

118

probability
A player tosses two fair coins. He wins rs 2 if 2 heads occur and rs 1 if 1 head occurs. On the other hand, he loses rs 3 if no heads occur. if the player plays 100 times.then the amount he wins______________(RS).

A player tosses two fair coins. He wins rs 2 if 2 heads occur and rs 1 if 1 head occurs. On the other hand, he loses rs 3 if no heads occur. if the player plays 100 times...

learner_geek

659 views

learner_geek asked Jan 20, 2019

2 votes

1 answer

119

Probability
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?

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...

ghostman23111

845 views

ghostman23111 asked Jan 19, 2019

3 votes

1 answer

120

GATE Overflow | Mock GATE | Test 1 | Question: 42
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? $(m+k)/(m+n+k)$ $(n+k)/(m+n+k)$ $m/(m+n+k)$ $m/(m+n)$

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 bal...

Ruturaj Mohanty

707 views

Ruturaj Mohanty asked Dec 27, 2018

tags	tag:apple
author	user:martin
title	title:apple
content	content:apple
exclude	-tag:apple
force match	+apple
views	views:100
score	score:10
answers	answers:2
is accepted	isaccepted:true
is closed	isclosed:true