A board of directors consists $n$ men and $\left( 10-n \right)$ women, where \(3\le n\le 7\

Question

A board of directors consists $n$ men and $\left( 10-n \right)$ women, where $3\le n\le 7$. A committee consisting $3$ randomly chosen people is to be formed. Let $W$ be the number of women in the committee. Show that $\mathrm{P}\left( W=1 \right)=\frac{n\left( n-1 \right)\left( 10-n \right)}{240}$ and find, in terms of $n$, the probability distribution of $W$.[4] Given $E\left( W \right)=2.1$, find $n$.[2] Hence, find $\mathrm{Var}\left( W \right)$.[1]

Accepted Answer

(ii) $3$ (iii) $\text{Var}(W) = \frac{49}{100}$

2018 VJC J2 MYE P1 Q10

2018 VJC J2 MYE P1 Q10

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