A man and a woman appear in an interview for | vedclass

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

Question

(A) Let $E_1$ be the event that the man is selected and $E_2$ be the event that the woman is selected.Given $P(E_1) = 1/4$ and $P(E_2) = 1/3$.The prob

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(A) Let $E_1$ be the event that the man is selected and $E_2$ be the event that the woman is selected.Given $P(E_1) = 1/4$ and $P(E_2) = 1/3$.The probability that the man is not selected is $P(\bar{E_1}) = 1 - P(E_1) = 1 - 1/4 = 3/4$.The probability that the woman is not selected is $P(\bar{E_2}) = 1 - P(E_2) = 1 - 1/3 = 2/3$.Since the events are independent,the probability that none of them will be selected is $P(\bar{E_1} \cap \bar{E_2}) = P(\bar{E_1}) 	imes P(\bar{E_2})$.Therefore,$P(\bar{E_1} \cap \bar{E_2}) = (3/4) 	imes (2/3) = 6/12 = 1/2$.

$A$ 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?

Similar Questions

Let $A$ and $B$ be events with $P(A)=\frac{1}{3}, P(B)=\frac{1}{4}$ and $P(A \cup B)=\frac{1}{2}$. Then which of the following statements is incorrect?

The probabilities of $A$ and $B$ dying in a year are $p$ and $q$ respectively. What is the probability that only one of them will be alive at the end of the year?

$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is:

$A$ lot consists of $12$ good pencils,$6$ with minor defects,and $2$ with major defects. $A$ pencil is chosen at random. The probability that this pencil is not defective is

The probability of getting a sum of $9$ when two dice are thrown is

Vedclass Test Series

Exam Paper Generator

Online Exam Module