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.

EASY

JEE Main/Advance

IMPORTANT

Earn 100

A father has $3$ children with at least one boy. The probability that he has $2$ boys and $1$ girl is

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Important Questions on Probability II

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 6

In a certain town,

40 %

of the people have brown hair,

25 %

have brown eyes, and

15 %

have both brown hair and brown eyes. If a person selected at random from the town has brown hair, the probability that he also has brown eyes is

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 7

Let

A

and

B

are events of an experiment and

P (A) = \frac{1}{4}, P (A \cup B) = \frac{1}{2}

, then value of

P (\frac{B}{A^{C}})

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 8

The probability that an automobile will be stolen and found within one week is

0.0006

.The probability that an automobile will be stolen is

0.0015

.The probability that a stolen automobile will be found in one week is

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 9

A pair of numbers is picked up randomly (without replacement) from the set

\{1, 2, 3, 5, 7, 11, 12, 13, 17, 19\}

. The probability that the number

11

was picked, given that the sum of the numbers was even, is nearly

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 10

All the jacks, queens, kings and aces of a regular

52

cards deck are taken out. The

16

cards are thoroughly shuffled and my opponent, a person who always tells the truth, simultaneously draws two cards at random and says, 'I hold at least one ace'. The probability that he holds two aces is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 11

One ticket is selected at random from

100

tickets numbered

00, 01, 02, \dots, 99

. Suppose

A

and

B

are the sum and product of the digit found on the ticket, respectively. Then

P (\frac{(A = 7)}{(B = 0)})

is given by

MEDIUM

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 12

Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second, is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 13

Cards are drawn one-by-one at random from a well shuffled pack of

52

playing cards until

2

aces are drawn from the first time. The probability that

18

draws are required for this is

A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is

Important Questions on Probability II

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A father has $3$ children with at least one boy. The probability that he has $2$ boys and $1$ girl is