Probability Ques 49

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 $R$.

Two students are selected from group $-Q$ at random one by one with replacement. What is the probability that both the students are females?

(1) $\frac{9}{25}$

(2) $\frac{16}{49}$

(3) $\frac{11}{30}$

(4) $\frac{25}{42}$

(5) $\frac{14}{34}$

Show Answer

Correct Answer: (1)

Solution: (1)

Total possible outcomes $=10$,

Favourable outcomes $=6$

Required probability $=\frac{{ }^{6} C_{1}}{{ }^{10} C_{1}} \times \frac{{ }^{6} C_{1}}{{ }^{10} C_{1}}=\frac{6}{10} \times \frac{6}{10}$ $=\frac{36}{100}$