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 $P(A|B) = \frac{P(A \cap B)}{P(B)}$:$P(E|F) = \frac{P(E \cap F)}{P(F)} = \frac{1/6}{1/3} = \frac{1}{6} 	imes 3 = \frac{1}{2}$.$P(F|E) = \frac{P(E \cap F)}{P(E)} = \frac{1/6}{1/2} = \frac{1}{6} 	imes 2 = \frac{1}{3}$.

List-$I$	List-$II$
$A$. $P(\frac{A}{B})$	$(i)$. $\frac{2}{15}$
$B$. $P(\bar{B})$	$(ii)$. $\frac{4}{15}$
$C$. $P(A \cap \bar{B})$	$(iii)$. $\frac{8}{15}$
$D$. $P(B \cap \bar{A})$	$(iv)$. $\frac{2}{3}$
	$(v)$. $\frac{3}{7}$

$A$ 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

If $P(A)=0.25, P(B)=0.55$ and $P(A \cup B)=0.65$,then $P(B' \mid A) =$ . . . . . . .

In a group of $14$ males and $6$ females, $8$ males and $3$ females are aged above $40 \text{ yr}$. The probability that a person selected at random from the group is aged above $40 \text{ yr}$, given that the selected person is a female, is:

$A$ die is thrown three times and the sum of the numbers obtained is $15$. What is the probability that the number $4$ appears in the first throw?

One card is drawn at random from a well-shuffled deck of $52$ cards. In which of the following cases are the events $E$ and $F$ independent?
$E:$ 'the card drawn is black'
$F:$ 'the card drawn is a king'

Vedclass Test Series

Exam Paper Generator

Online Exam Module