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.

Answer 1

The correct answer is: \(\frac{44}{91}\)
S={12 good oranges, 3 bad oranges}
\(⇒n(S)=15\)
Probability that first orange drawn is good\(=\frac{12}{15}\)
Probability that second orange is drawn is good\(=\frac{11}{14}\)
Probability that third orange is drawn is good when both the first and second are good\(=\frac{10}{13}\)
P (a box is approved)\(=\frac{C(12,3)}{C(15,3)}\)
\(=\frac{12×11×10}{15×14×13}\)
\(=\frac{44}{91}\)