Two students appeared simultaneously for an e | vedclass

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

Question

(D) Let $A$ be the event that the first student qualifies and $B$ be the event that the second student qualifies. Given $P(A) = \frac{1}{4}$ and $P(B)

Vedclass · Accepted Answer

$\frac{11}{20}$

Vedclass · Answer

(D) Let $A$ be the event that the first student qualifies and $B$ be the event that the second student qualifies. Given $P(A) = \frac{1}{4}$ and $P(B) = \frac{2}{5}$. Since the events are independent,the probability that neither qualifies is $P(A^c \cap B^c) = P(A^c) 	imes P(B^c)$. $P(A^c) = 1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$. $P(B^c) = 1 - P(B) = 1 - \frac{2}{5} = \frac{3}{5}$. Probability that neither qualifies = $\frac{3}{4} 	imes \frac{3}{5} = \frac{9}{20}$. Probability that at least one qualifies = $1 - P(	ext{neither qualifies}) = 1 - \frac{9}{20} = \frac{11}{20}$.

Similar Questions

The probability of a sure event is

$A$ man and a woman appear in an interview for two vacancies in the same post. The probability of the man's selection is $1/4$ and that of the woman's selection is $1/3$. What is the probability that none of them will be selected?

$A$ bag contains $3$ white,$3$ black and $2$ red balls. Three balls are drawn one by one without replacement. The probability that the third ball is red is:

An integer is chosen at random and squared. The probability that the last digit of the square is $1$ or $5$ is

The probabilities of three students solving a question are $\frac{1}{2}, \frac{1}{4},$ and $\frac{1}{6}$ respectively. What is the probability that the question is solved?

Vedclass Test Series

Exam Paper Generator

Online Exam Module