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 $10$ are good and $5$ are bad ones will be approved for sale.

• A. $\frac{24}{91}$
• B. $\frac{24}{91}$
• C. $\frac{12}{91}$
• D. $\frac{10}{91}$

Answer 1

The correct option is A $\frac{24}{91}$

$\because$ box is approved for the sale
$\therefore$ P(selecting good oranges)$=\frac{{}^{10}{C}_3}{{}^{15}{C}_3}=\frac{24}{91}$