Solutions - 5050-03

(1) Compute $P [A]$ and $P [B]$ :

Total ways to choose 2 from 5: $(\binom{5}{2}) = 10$

P [A] = \frac{(\binom{2}{2})}{(\binom{5}{2})} = \frac{1}{10}, P [B] = \frac{(\binom{3}{2})}{(\binom{5}{2})} = \frac{3}{10}

(2) Check independence:

$P [A \cap B] = 0$ since selecting 2 people cannot yield both “2 more qualified” and “2 less qualified” simultaneously.

P [A \cap B] = 0 \neq \frac{1}{10} \cdot \frac{3}{10} = P [A] \cdot P [B]

So $A$ and $B$ are not independent.

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