Let A and B be two events such that P A ∪ B = 1 6 , P A ∩ B = 1 4 , and P A = 1 4 , where A ¯ stands for complement of event A . Then events A and B are

independent but not equally likely.

mutually exclusive and independent.

equally likely but not independent.

equally likely and mutually exclusive.

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JEE Main/Advance

IMPORTANT

Earn 100

Three critics review a book. Odds in favor of the book are $5 : 2, 4 : 3,$ and $3 : 4$ , respectively, for the three critics. The probability that majority are in favor of the book is

36.36% studentsanswered this correctly

Important Questions on Probability II

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 32

A

and

B

play a game of tennis. The situation of the game is as follows: if one scores two consecutive points after a deuce, he wins; if loss of a point is followed by win of a point, it is deuce. The chance of a server to win a point is

\frac{2}{3}

. The game is at deuce and

A

is serving. Probability that

A

will win the match is (serves are changed after each game)

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 33

An unbiased cubic die marked with

1, 2, 2, 3, 3, 3

is rolled

3

times. The probability of getting a total score of

4

6

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 34

A fair die is tossed repeatedly.

A

wins if it is

1

2

on two consecutive tosses and

B

wins if it is

3, 4, 5

6

on two consecutive tosses. The probability that

A

wins if the die is tossed indefinitely, is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 35

Whenever horses

a, b, c

race together, their respective probabilities of winning the race are

0.3, 0.5

and

0.2

, respectively. If they race three times, the probability that "the same horse will win all the three race" and the probability that "

a, b, c

each wins one race" are, respectively.

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 36

A man alternately tosses a coin and throws a die beginning with the coin. The probability that he gets a head in the coin before he gets a

5

6

in the dice is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 37

p

is the probability that a man aged

x

will die in a year, then the probability that out of

n

men

A_{1}, A_{2}, \dots, A_{n}

each aged

x, A_{1}

will die in an year and be the first to die is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 38

Thirty-two players ranked

1

32

are playing in a knockout tournament. Assume that in every match between any two players, the better-ranked player wins, the probability that ranked

1

and

2

players are winner and runner up, respectively, is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 39

A pair of unbiased dice is rolled together till a sum of either

5

7

is obtained. The probability that

5

comes before

7

Three critics review a book. Odds in favor of the book are 5:2, 4:3, and 3:4, respectively, for the three critics. The probability that majority are in favor of the book is

Important Questions on Probability II

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Three critics review a book. Odds in favor of the book are $5 : 2, 4 : 3,$ and $3 : 4$ , respectively, for the three critics. The probability that majority are in favor of the book is