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Solve the following.
A and B appeared for an interview for two vacancies. The probability of A's selection is 4/5 and…
$A$ and $B$ appeared for an interview for two vacancies. The probability of $A$'s selection is $\frac{4}{5}$ and $B$'s selection is $\frac{1}{3}$. Find the probability that none of them will be selected.
Answer
Answer
$P(A') = 1 - \frac{4}{5} = \frac{1}{5}$ and $P(B') = 1 - \frac{1}{3} = \frac{2}{3}$.
Assuming the selections are independent, $P(A' \cap B') = \frac{1}{5} \times \frac{2}{3} = \frac{2}{15}$.
Final answer: $\frac{2}{15}$