Let A and B be independent events with P ( A ) = 1 4 , and P ( A ∪ B ) = 2 P ( B ) − P ( A ) . Find P A B .

Given A and B are Independent events P ( A ) = 1 4 & P ( A ∪ B ) = 2 P ( B ) - P ( A ) Now, P A B = P A ∩ B P B = P A P B P B = P ( A ) = 1 4 .

Let A and B be independent events with P ( A ) = 1 4 , and P ( A ∪ B ) = 2 P ( B ) − P ( A ) . Find P A B .

Given A and B are Independent events P ( A ) = 1 4 & P ( A ∪ B ) = 2 P ( B ) - P ( A ) Now, P A B = P A ∩ B P B = P A P B P B = P ( A ) = 1 4 .

EASY

11th Maharashtra Board

IMPORTANT

Earn 100

Let $A$ and $B$ be independent events with $P (A) = \frac{1}{4}$ , and $P (A \cup B) = 2 P (B) - P (A)$ . Find $P (\frac{A}{B})$ .

Important Questions on Probability

HARD

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 12

Let

A

and

B

be independent events with

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

, and

P (A \cup B) = 2 P (B) - P (A)

. Find

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

HARD

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 13

Find the probability that a year selected will have

53

Wednesdays.

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 14

The chances of $P, Q$ and $R$ getting selected as principal of a college are $\frac{2}{5}, \frac{2}{5}, \frac{1}{5}$ respectively. Their chances of introducing $I T$ in the college are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ respectively. Find the probability that $I T$ is introduced in the college after one of them is selected as a principal.

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 14

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 15

Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one by one, at random and without replacement. What is the probability that we are lucky and fine both of the defective fuses in the first two tests?

HARD

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 16

For three events

A, B

and

C

, we know that

A

and

C

are independent,

B

and

C

are independent,

A

and

B

are disjoint,

P (A \cup C) = \frac{2}{3}

P (B \cup C) = \frac{3}{4}

P (A \cup B \cup C) = \frac{11}{12}

. Find

P (A), P (B)

and

P (C)

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 17

The ratio of Boys to Girls in a college is

3 : 2

and

3

girls out of

500

and

2

boys out of

50

of that college are good singers. A good singer is chosen what is the probability that the chosen singer is a girl?

MEDIUM

11th Maharashtra Board

IMPORTANT

Mathematics and Statistics (Arts & Science) Part 1>Chapter 9 - Probability>MISCELLANEOUS EXERCISE - 9>Q 18

A

and

B

throw a die alternatively till one of them gets a

3

and wins the game. Find the respective probabilities of winning. (Assuming

A

begins the game).

Let A and B be independent events with P(A)=14, and P(A∪B)=2P(B)−P(A). Find PAB.

Important Questions on Probability

Learn and Prepare for any exam you want !

Let $A$ and $B$ be independent events with $P (A) = \frac{1}{4}$ , and $P (A \cup B) = 2 P (B) - P (A)$ . Find $P (\frac{A}{B})$ .