2015 SRJC P2 Q9

In a calculators manufacturing factory, it is found that \(1.5\%\) of the calculators produced are defective.

In a random sample of \(90\) calculators, find the probability that

1. there are exactly \(2\) defective calculators,[1]
2. the \({{90}^{\mathrm{th}}}\) calculator is the second defective calculator given that there are exactly \(2\) defective calculators in that sample.[3]

The calculators are packed in boxes of \(90\).

3. Find the probability that not more than \(1\) box of calculators, out of \(60\) boxes, contain more than \(2\) defective calculators.[5]