The probabilities of winning the race by two | vedclass

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Question

(A) Let $P(A)$ be the probability that athlete $A$ wins the race,so $P(A) = \frac{1}{5}$.Let $P(B)$ be the probability that athlete $B$ wins the race,

Vedclass · Accepted Answer

$\frac{3}{5}$

Vedclass · Answer

(A) Let $P(A)$ be the probability that athlete $A$ wins the race,so $P(A) = \frac{1}{5}$.Let $P(B)$ be the probability that athlete $B$ wins the race,so $P(B) = \frac{1}{4}$.The probability that athlete $A$ does not win is $P(A') = 1 - P(A) = 1 - \frac{1}{5} = \frac{4}{5}$.The probability that athlete $B$ does not win is $P(B') = 1 - P(B) = 1 - \frac{1}{4} = \frac{3}{4}$.Since the events of winning are independent,the probability that neither of them wins is $P(A' \cap B') = P(A') 	imes P(B') = \frac{4}{5} 	imes \frac{3}{4} = \frac{3}{5}$.

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}$ respectively. The probability of winning by neither of them is:

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