Two friends A and B apply for a job in the sa | vedclass

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

Question

(B) Given: $P(A) = \frac{2}{5}$ and $P(B) = \frac{4}{7}$.We need to find the probability that exactly one of them is selected.This is given by the for

Vedclass · Accepted Answer

$\frac{18}{35}$

Vedclass · Answer

(B) Given: $P(A) = \frac{2}{5}$ and $P(B) = \frac{4}{7}$.We need to find the probability that exactly one of them is selected.This is given by the formula: $P(	ext{exactly one}) = P(A \cap B') + P(A' \cap B)$.Since the events are independent,$P(A \cap B') = P(A) 	imes P(B')$ and $P(A' \cap B) = P(A') 	imes P(B)$.Here,$P(A') = 1 - P(A) = 1 - \frac{2}{5} = \frac{3}{5}$ and $P(B') = 1 - P(B) = 1 - \frac{4}{7} = \frac{3}{7}$.Substituting the values:$P(	ext{exactly one}) = \left(\frac{2}{5} 	imes \frac{3}{7}ight) + \left(\frac{3}{5} 	imes \frac{4}{7}ight)$$= \frac{6}{35} + \frac{12}{35}$$= \frac{18}{35}$.

Two friends $A$ and $B$ apply for a job in the same company. The probability of $A$ getting selected is $\frac{2}{5}$ and that of $B$ is $\frac{4}{7}$. Then the probability that one of them is selected is:

Similar Questions

In each of the following experiments,specify the appropriate sample space: $A$ boy has a $1$ rupee coin,a $2$ rupee coin,and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket,one after the other.

Four dice (six-faced) are rolled. The number of possible outcomes in which at least one die shows $2$ is

Events $E$ and $F$ are such that $P(\text{not } E \text{ and not } F) = 0.25$. State whether $E$ and $F$ are mutually exclusive.

$A$ bag contains $9$ discs of which $4$ are red,$3$ are blue,and $2$ are yellow. The discs are similar in shape and size. $A$ disc is drawn at random from the bag. Calculate the probability that it will be either red or blue.

$A$ die is thrown. Find the probability of the following event: $A$ number less than or equal to $1$ will appear.

Vedclass Test Series

Exam Paper Generator

Online Exam Module