Probability Ques 48

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 from each of groups B and R separately. What is the probability that one student is male and other is female?

(1) $\frac{19}{36}$

(2) $\frac{15}{28}$

(3) $\frac{12}{35}$

(4) $\frac{17}{31}$

(5) $\frac{18}{39}$

Show Answer

Correct Answer: (1)

Solution: (1)

Required probability $=\left(\left(\frac{7}{12}\right) \times\left(\frac{6}{9}\right)+\left(\frac{5}{12}\right) \times\left(\frac{3}{9}\right)\right)$ $=\frac{7}{18}+\frac{5}{36}=\frac{14+5}{36}=\frac{19}{36}$