In a school,there are 1000 students,out of wh | vedclass

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

Question

(A) Let $E$ be the event that the chosen student studies in class $XII$ and $F$ be the event that the chosen student is a girl. We are given that the

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(A) Let $E$ be the event that the chosen student studies in class $XII$ and $F$ be the event that the chosen student is a girl. We are given that the total number of students is $1000$ and the number of girls is $430$. Thus,$P(F) = \frac{430}{1000} = 0.43$. It is given that $10\%$ of the girls study in class $XII$. So,the number of girls studying in class $XII$ is $10\% 	ext{ of } 430 = \frac{10}{100} 	imes 430 = 43$. Therefore,the number of students who are girls and study in class $XII$ is $43$. Thus,$P(E \cap F) = \frac{43}{1000} = 0.043$. We need to find the conditional probability $P(E|F)$,which is the probability that a student studies in class $XII$ given that the student is a girl. Using the formula for conditional probability: $P(E|F) = \frac{P(E \cap F)}{P(F)}$. Substituting the values: $P(E|F) = \frac{0.043}{0.43} = 0.1$.

In a school,there are $1000$ students,out of which $430$ are girls. It is known that out of $430$,$10\%$ of the girls study in class $XII$. What is the probability that a student chosen randomly studies in class $XII$ given that the chosen student is a girl?

Similar Questions

$A$ and $B$ are two events such that $P(A) \neq 0$. Find $P(B | A)$ if $A \cap B = \phi$.

Evaluate $P(A \cup B)$,if $2 P(A) = P(B) = \frac{5}{13}$ and $P(A|B) = \frac{2}{5}$.

If $6 P(A) = 8 P(B) = 14 P(A \cap B) = 1$,then $P(A' \mid B) = $ . . . . . . .

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

Consider the experiment of throwing a die. If a multiple of $3$ comes up,throw the die again,and if any other number comes,toss a coin. Find the conditional probability of the event 'the coin shows a tail',given that 'at least one die shows a $3$'.

Vedclass Test Series

Exam Paper Generator

Online Exam Module