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.

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

Let $A, B, C$ be three mutually independent events. Consider the two statements $S_{1}$ and $S_{2}$ .

$S_{1} : A$ and $B \cup C$ are independent.

$S_{2} : A$ and $B \cap C$ are independent.

Then

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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 19

Three ships

A, B

and

C

sail from England to India. If the ratio of their arriving safely are

2 : 5, 3 : 7

and

6 : 11

, respectively, then the probability of all the ships for arriving safely is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 20

Cards are drawn one by one without replacement from a pack of

52

cards. The probability that

10

cards will precede the first ace is

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 21

Five horses are in a race. Mr.

A

selects two of the horses at random and bets on them. The probability that Mr.

A

selected the winning horse, is

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 22

Let

A

and

B

be two events such that

P (A \cup B) = \frac{1}{6}, P (A \cap B) = \frac{1}{4}

, and

P (A) = \frac{1}{4}

, where

\bar{A}

stands for complement of event

A

. Then events

A

and

B

are

HARD

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 23

A class consists of

80

students

25

of them are girls and

55

boys. If

10

are rich and remaining poor and also

20

of them are intelligent, then the probability of selecting intelligent rich girls is

EASY

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IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 24

Events

A

and

C

are independent. If the probabilities relating

A, B

and

C

are

P (A) = \frac{1}{5}, P (B) = \frac{1}{6}; P (A \cap C) = \frac{1}{20}; P (B \cup C) = \frac{3}{8}

. Then,

EASY

JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 25

Let

A

and

B

two events. Suppose

P (A) = 0.4, P (B) = p,

and

P (A \cup B) = 0.7

. The value of

p

for which

A

and

B

are independent is

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JEE Main/Advance

IMPORTANT

Mathematics for Joint Entrance Examination JEE (Advanced) Algebra>Chapter 14 - Probability II>Exercises>Q 26

A box contains

2

black,

4

white, and

3

red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of

2

black,

4

white, and

3

red is

Let A, B, C be three mutually independent events. Consider the two statements S1 and S2. S1: A and B∪C are independent. S2: A and B∩C are independent. Then

Important Questions on Probability II

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Let $A, B, C$ be three mutually independent events. Consider the two statements $S_{1}$ and $S_{2}$ .

$S_{1} : A$ and $B \cup C$ are independent.

$S_{2} : A$ and $B \cap C$ are independent.

Then