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(D) Let $A$ be the event that the first student qualifies and $B$ be the event that the second student qualifies. Given $P(A) = \frac{1}{4}$ and $P(B)

Vedclass · Accepted Answer

$\frac{11}{20}$

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(D) Let $A$ be the event that the first student qualifies and $B$ be the event that the second student qualifies. Given $P(A) = \frac{1}{4}$ and $P(B) = \frac{2}{5}$. Since the events are independent,the probability that neither qualifies is $P(A^c \cap B^c) = P(A^c) 	imes P(B^c)$. $P(A^c) = 1 - P(A) = 1 - \frac{1}{4} = \frac{3}{4}$. $P(B^c) = 1 - P(B) = 1 - \frac{2}{5} = \frac{3}{5}$. Probability that neither qualifies = $\frac{3}{4} 	imes \frac{3}{5} = \frac{9}{20}$. Probability that at least one qualifies = $1 - P(	ext{neither qualifies}) = 1 - \frac{9}{20} = \frac{11}{20}$.

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