Question

Family $A$ has $6$ members of which $4$ are males and $2$ are females & family $B$ has $5$ members of both genders. (Assume it is equi-probable for a member of unknown gender to be a male or female).

Let two members be selected, one from family $A$ & other from family $B$. Probability that selected members includes one male and one female is equal to

• A. $\frac{1}{3}$
• B. $\frac{23}{40}$
• C. $\frac{21}{40}$
• D. $0.45$

Answer 1

Answer: (D)

$0.45$

From Family $A$ it can be selected by,

$\frac{{}^4{C}_1+{}^2{C}_1}{{}^{11}{C}_2}$

and from Family $B$, $\frac{{}^5{C}_2}{{}^{11}{C}_2}$

$\Rightarrow \frac{{}^4{C}_2+{}^2{C}_1+{}^5{C}_2}{{}^{11}{C}_2}=\mathrm{0.45.}$

Hence, the answer is $\mathrm{0.45.}$