6 married

Six married couples are in a room. If two people are chosen at random. Find the probability that;
a). they are married.
b). one is male, and one is female.

Correct answer:

a =  0.0909
b =  0.5455

Step-by-step explanation:

$$\begin{gathered} C_2(12)=\left(\genfrac{}{}{0ex}{}{12}{2}\right)=\frac{12!}{2!(12-2)!}=\frac{12\cdot 11}{2\cdot 1}=66 \\ n=\left(\genfrac{}{}{0ex}{}{12}{2}\right)=66 \\ {C}_1(6)=\left(\genfrac{}{}{0ex}{}{6}{1}\right)=\frac{6!}{1!(6-1)!}=\frac{6}{1}=6 \\ a=\frac{\left(\genfrac{}{}{0ex}{}{6}{1}\right)\cdot 1}{n}=\frac{6\cdot 1}{66}=\frac{1}{11}=0.0909 \end{gathered}$$

$b=\frac{\left(\genfrac{}{}{0ex}{}{6}{1}\right)\cdot \left(\genfrac{}{}{0ex}{}{6}{1}\right)}{n}=\frac{6\cdot 6}{66}=\frac{6}{11}=0.5455$

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