For two events A and B,if P(A) = P(A|B) = fra | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $P(A) = \frac{1}{4}$ and $P(A|B) = \frac{1}{4}$.Since $P(A|B) = P(A)$,the events $A$ and $B$ are independent.For independent events,$P(B|A)

Vedclass · Accepted Answer

All of the above

Vedclass · Answer

(D) Given $P(A) = \frac{1}{4}$ and $P(A|B) = \frac{1}{4}$.Since $P(A|B) = P(A)$,the events $A$ and $B$ are independent.For independent events,$P(B|A) = P(B) = \frac{1}{2}$.Now,check each option:$(a)$ Since $P(A|B) = P(A)$,$A$ and $B$ are independent. This is correct.$(b)$ For independent events,$P(A'|B) = P(A') = 1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$. This is correct.$(c)$ For independent events,$P(B'|A') = P(B') = 1 - P(B) = 1 - \frac{1}{2} = \frac{1}{2}$. This is correct.Since all statements are correct,the answer is $(d)$.

For two events $A$ and $B$,if $P(A) = P(A|B) = \frac{1}{4}$ and $P(B|A) = \frac{1}{2}$,then

Similar Questions

Out of $30$ consecutive numbers,$2$ are chosen at random. The probability that their sum is odd,is

What is the chance that a leap year,selected at random,will contain $53$ Sundays (in $/7$)?

$A$ bag contains $7$ black and $5$ white balls. $A$ ball is drawn out and replaced in the bag. Then a ball is drawn again. What is the probability that the first ball was white and the second black?

Study the given information carefully and answer the questions that follow: $A$ basket contains $4$ red,$5$ blue and $3$ green marbles. If $2$ marbles are drawn at random,what is the probability that both are red?

From a pack of $52$ cards,one card is drawn at random. The probability that it is either a king or a queen is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module