Probability Ques 47

Question-

Directions : The following paragraph shows the details of male and female students in five different groups. Consider the following paragraph and answer the questions given below :

There are 5 different groups $A$, $B, P, Q$ and $R$.

There are 9 males and 5 females in group $A$.

There are 5 males and 7 females in group B.

There are 7 males and 4 females in group $P$.

There are 4 males and 6 females in group $Q$.

There are 6 males and 3 females in group $R$.

One student is selected at random from either of the groups $P$ or $A$. What is the probability that the student is a male?

(1) $\frac{201}{308}$

(2) $\frac{157}{308}$

(3) $\frac{197}{308}$

(4) $\frac{212}{308}$

(5) $\frac{177}{308}$

Show Answer

Correct Answer: (3)

Solution: (3)

Required probability $=\frac{1}{2}$ (selection of one boy from $P$ + selection of boy from A) $=\frac{1}{2}\left(\frac{9}{14}+\frac{7}{11}\right)$ $=\frac{1}{2}\left(\frac{99+98}{154}\right)$ $=\frac{197}{308}$