GATE CS Conditional Probability and Bayes Theorem questions

Practise Conditional Probability and Bayes Theorem questions for GATE CS. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

Define the sample space and events first. Distinguish independent events from conditional probabilities, and check that the final probability lies between zero and one.

13 on this page

SubjectTopicYearType

Suppose an unbiased coin is tossed

6

times. Each coin toss is independent of all previous coin tosses. Let

E_{1}

be the event that among the second, fourth, and sixth coin tosses, there are at least two heads. Let

E_{2}

be the event that among the first, second, third, and fifth coin tosses, there are equal number of heads and tails. The …

10

15

blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to

3

decimal places) that both balls drawn are red is ___________.

(\textsf{S})

transmits a signal, which can be one of the two kinds:

H

L

with probabilities

0.1

0.9

respectively, to a receiver

(\textsf{R})

. In the graph below, the weight of edge

(u,v)

is the probability of receiving

v

u

is transmitted, where

u,v \in \{H,L\}

. For example, the probability that the …

Consider Guwahati,

(G)

(D)

whose temperatures can be classified as high

(H)

(M)

(L)

P(H_G)

denote the probability that Guwahati has high temperature. Similarly,

P(M_G)

P(L_G)

denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use …

P

Q

are considering to apply for a job. The probability that

P

applies for the job is

\dfrac{1}{4},

the probability that

P

applies for the job given that

Q

applies for the job is

\dfrac{1}{2},

and the probability that

Q

applies for the job given that

P

applies for the job is

\dfrac{1}{3}.

Then the probability that …

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

0.7

, and given that it is of Type

2

0.4

. The probability that an LED bulb chosen uniformly at random lasts more than

100

hours is _________.

Suppose a fair six-sided die is rolled once. If the value on the die is

1, 2,

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

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

An unbalanced dice (with

6

faces, numbered from

1

6

) is thrown. The probability that the face value is odd is

90\%

of the probability that the face value is even. The probability of getting any even numbered face is the same. If the probability that the face is even given that it is greater than

3

0.75

, which one of the …

Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is

0.6

. If she studies mathematics on a day, then the probability that she studies computer science the next day is

0.4

. Given that Aishwarya studies computer science on Monday, …

P

2

3

blue balls and box

Q

3

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

Q

\dfrac{1}{3}

\dfrac{2}{3}

P(E)

denote the probability of the event

E

P(A) = 1

P(B) =\dfrac{1}{2}

, the values of

P(A\mid B)

P(B\mid A)

respectively are

A

B

be any two arbitrary events, then, which one of the following is TRUE?