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(A) Let $A, B,$ and $C$ be the events that the first,second,and third drawn oranges are good,respectively.The probability that the first orange drawn

Vedclass · Accepted Answer

$\frac{44}{91}$

Vedclass · Answer

(A) Let $A, B,$ and $C$ be the events that the first,second,and third drawn oranges are good,respectively.The probability that the first orange drawn is good is $P(A) = \frac{12}{15}$.Since the oranges are drawn without replacement,the total number of oranges and the number of good oranges decrease by $1$ for each subsequent draw.The probability that the second orange is good,given the first was good,is $P(B|A) = \frac{11}{14}$.The probability that the third orange is good,given the first two were good,is $P(C|A \cap B) = \frac{10}{13}$.The box is approved for sale if all three oranges are good. Thus,the required probability is $P(A \cap B \cap C) = P(A) 	imes P(B|A) 	imes P(C|A \cap B)$.$P(A \cap B \cap C) = \frac{12}{15} 	imes \frac{11}{14} 	imes \frac{10}{13} = \frac{4}{5} 	imes \frac{11}{14} 	imes \frac{10}{13} = \frac{440}{910} = \frac{44}{91}$.Therefore,the probability that the box is approved for sale is $\frac{44}{91}$.

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