Two events A and B are given. If P(A) = frac{ | vedclass

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

Question

(B) Given that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$.We know the definition of conditional probability: $P(B|A) = \fr

Vedclass · Accepted Answer

$1/3$

Vedclass · Answer

(B) Given that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$.We know the definition of conditional probability: $P(B|A) = \frac{P(A \cap B)}{P(A)}$.Substituting the known values: $\frac{2}{3} = \frac{P(A \cap B)}{1/4}$.Therefore,$P(A \cap B) = \frac{2}{3} 	imes \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$.Now,use the definition of conditional probability for $P(A|B)$: $P(A|B) = \frac{P(A \cap B)}{P(B)}$.Substituting the values: $\frac{1}{2} = \frac{1/6}{P(B)}$.Solving for $P(B)$: $P(B) = \frac{1/6}{1/2} = \frac{1}{6} 	imes 2 = \frac{2}{6} = \frac{1}{3}$.Thus,the value of $P(B)$ is $\frac{1}{3}$.

Two events $A$ and $B$ are given. If $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$,then what is the value of $P(B)$?

Similar Questions

If $A$ and $B$ are two events such that $P(\bar{A})=0.3, P(B)=0.4$ and $P(A \cap \bar{B})=0.5$, then $P(B \mid A \cup \bar{B})=$

If $A$ and $B$ are two independent events,then $P\left( \frac{A}{B} \right) = $

If $P(A) = \frac{7}{13}$,$P(B) = \frac{9}{13}$ and $P(A \cap B) = \frac{4}{13}$,evaluate $P(A | B)$.

It is given that $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A|B) = \frac{1}{2}$,and $P(B|A) = \frac{2}{3}$. Then $P(B) = $?

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes,the number of outcomes that $B$ must have so that $A$ and $B$ are independent,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module