Probability Ques 46

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 at random from the Group B without replacement. What is the probability that one is male and another is female?

(1) $\frac{35}{66}$

(2) $\frac{25}{11}$

(3) $\frac{20}{11}$

(4) $\frac{13}{11}$

(5) $\frac{33}{11}$

Show Answer

Correct Answer: (1)

Solution: (1)

Required probability $=$ selec tion of one boy and then girl + selection of one girl and then boy $=\left[\left(\frac{7}{12} \times \frac{5}{11}\right)+\left(\frac{5}{12} \times \frac{7}{11}\right)\right]$ $=\frac{35}{132}+\frac{35}{132}=\frac{70}{132}=\frac{35}{66}$