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# A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected.

Q.3   A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing $\inline 15$ oranges out of which $\inline 12$ are good and $\inline 3$ are bad ones will be approved for sale.

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Total oranges = 15

Good oranges = 12

Bad oranges = 3

Let  $P(A)$ be the probability that first orange is good.

The, we have

$P(A)= \frac{12}{15}=\frac{4}{5}$

Let  $P(B)$ be the probability that second orange is good.

$P(B)=\frac{11}{14}$

Let  $P(C)$ be the probability that third orange is good.

$P(C)=\frac{10}{13}$

The probability that a box  will be approved for sale $=P(A).P(B).P(C)$

$=\frac{4}{5}.\frac{11}{14}.\frac{10}{13}$

$=\frac{44}{91}$

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