In a random experiment,events A and B are suc | vedclass

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

Question

(A) We know that the conditional probability formula is given by $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.Substituting the given values,we get $P(A \c

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(A) We know that the conditional probability formula is given by $P(B \mid A) = \frac{P(A \cap B)}{P(A)}$.Substituting the given values,we get $P(A \cap B) = P(B \mid A) 	imes P(A) = \frac{2}{3} 	imes \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$.Now,we use the conditional probability formula for $P(A \mid B)$:$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$.Rearranging for $P(B)$,we get $P(B) = \frac{P(A \cap B)}{P(A \mid B)}$.Substituting the values,$P(B) = \frac{1/6}{1/2} = \frac{1}{6} 	imes 2 = \frac{1}{3}$.

In a random experiment,events $A$ and $B$ are such that $P(A) = \frac{1}{4}$,$P(A \mid B) = \frac{1}{2}$,and $P(B \mid A) = \frac{2}{3}$. Find $P(B)$.

Similar Questions

Let $A$ and $B$ be two events with $P(A^{C}) = 0.3$, $P(B) = 0.4$, and $P(A \cap B^{C}) = 0.5$. Then $P(B \mid A \cup B^{C})$ is equal to

Two cards are drawn one by one from a pack of cards. The probability of getting the first card as an ace and the second as a coloured card is (without replacement).

For two events $A$ and $B$,$P(A) \neq 0$ and $P(B \mid A) = 1$,then . . . . . . .

If $A$ and $B$ are two events such that $A \subset B$ and $P(B) \neq 0$,then which of the following is correct?

If $A$ and $B$ are two events of a random experiment such that $P(A)=0.6$,$P(B)=0.3$,and $P(A \mid B)=0.5$,then $P(\bar{B} \mid \bar{A})=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module