A box of oranges is inspected by examining three randomly selecte… - Vidyadip

Question

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 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

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Answer

There are 15 organes out of which 12 are good and 3 are bad.
Three oranges selected without replacement are drawn and if they found good the box is approved for salw.
A = First orange good
B = Second orange good
B = Third orange good
P (All three oranges are good)
$=\text{P(A)}\text{ P}\Big(\frac{\text{B}}{\text{A}}\Big)\text{ P}\Big(\frac{\text{C}}{\text{A}\cap\text{B}}\Big)$
$=\frac{12}{15}\times\frac{11}{14}\times\frac{10}{13}$
$=\frac{44}{91}$
Required probability $=\frac{44}{91}$

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