If E_1 and E_2 are two events of a sample spa | vedclass

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

Question

(D) Given that $P(E_1) = \frac{1}{4}$ and $P(E_2 \mid E_1) = \frac{1}{2}$.Using the definition of conditional probability,$P(E_1 \cap E_2) = P(E_1)

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(D) Given that $P(E_1) = \frac{1}{4}$ and $P(E_2 \mid E_1) = \frac{1}{2}$.Using the definition of conditional probability,$P(E_1 \cap E_2) = P(E_1) 	imes P(E_2 \mid E_1) = \frac{1}{4} 	imes \frac{1}{2} = \frac{1}{8}$.We are also given $P(E_1 \mid E_2) = \frac{1}{4}$.By definition,$P(E_1 \mid E_2) = \frac{P(E_1 \cap E_2)}{P(E_2)}$,so $\frac{1}{4} = \frac{1/8}{P(E_2)}$.This implies $P(E_2) = \frac{1/8}{1/4} = \frac{1}{2}$.We need to find $P(\bar{E}_1 \mid E_2)$.Using the property of conditional probability,$P(\bar{E}_1 \mid E_2) = 1 - P(E_1 \mid E_2)$.Substituting the given value,$P(\bar{E}_1 \mid E_2) = 1 - \frac{1}{4} = \frac{3}{4}$.

If $E_1$ and $E_2$ are two events of a sample space such that $P(E_1) = \frac{1}{4}$,$P(E_2 \mid E_1) = \frac{1}{2}$,and $P(E_1 \mid E_2) = \frac{1}{4}$,then $P(\bar{E}_1 \mid E_2) = $

Similar Questions

If $P(A) = \frac{1}{2}$,$P(B) = \frac{1}{3}$ and $P(A \cap B) = \frac{1}{4}$,then $P(B/A) = $

If $A$ and $B$ are two independent events such that $P(A \cap B') = \frac{3}{25}$ and $P(A' \cap B) = \frac{8}{25}$,then $P(A) = $

Ten cards numbered $1$ to $10$ are placed in a box,mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3,$ what is the probability that it is an even number (in $/7$)?

$A$ bag contains $3$ red and $7$ black balls. Two balls are taken out at random,without replacement. If the first ball taken out is red,what is the probability that the second ball taken out is also red?

If $A$ and $B$ are any two events such that $P(A) + P(B) - P(A \cap B) = P(A)$, then $\dots \dots \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module