A fair die is rolled. Consider events E={1,3, | vedclass

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

Question

(A) When a fair die is rolled,the sample space $S$ is $S=\{1, 2, 3, 4, 5, 6\}$.Given events are $E=\{1, 3, 5\}$ and $F=\{2, 3\}$.The intersection of $

Vedclass · Accepted Answer

$P(E|F) = \frac{1}{2}, P(F|E) = \frac{1}{3}$

Vedclass · Answer

(A) When a fair die is rolled,the sample space $S$ is $S=\{1, 2, 3, 4, 5, 6\}$.Given events are $E=\{1, 3, 5\}$ and $F=\{2, 3\}$.The intersection of $E$ and $F$ is $E \cap F = \{3\}$.The probabilities are $P(E) = \frac{3}{6} = \frac{1}{2}$ and $P(F) = \frac{2}{6} = \frac{1}{3}$.The probability of the intersection is $P(E \cap F) = \frac{1}{6}$.Using the formula for conditional probability $P(A|B) = \frac{P(A \cap B)}{P(B)}$:$P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{1/6}{1/3} = \frac{1}{6} 	imes 3 = \frac{1}{2}$.$P(F|E) = \frac{P(E \cap F)}{P(E)} = \frac{1/6}{1/2} = \frac{1}{6} 	imes 2 = \frac{1}{3}$.

$A$ fair die is rolled. Consider events $E=\{1,3,5\}, F=\{2,3\}$ and $G=\{2,3,4,5\}$. Find $P(E | F)$ and $P(F | E)$.

Similar Questions

$P(A / A \cap B) + P(B / A \cap B) =$

Let $A$ and $B$ be two events such that $P(A) = \frac{3}{8}$, $P(B) = \frac{5}{8}$ and $P(A \cup B) = \frac{3}{4}$. Then $P(A'|B) - P(A|B) =$ . . . . . .

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

If $A$ and $B$ are events such that $P(A) > 0$ and $P(B) \neq 1$,then $P(A \mid B^{\prime}) = $ . . . . . . .

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module