2024 ASRJC H1 Q6

In the mass production of bolts, it is found that \(5\)% are defective. Bolts are selected at random and put into packets of ten.

A packet is sold at reduced price if more than \(1\) bolt is defective.

1. Find the probability that a randomly selected packet of bolts is sold at reduced price.[2]
2. Find the probability that two randomly chosen packets each will be sold at reduced price.[2]

Last Monday, \(20\) packets of bolts were sold.

3. Find the probability that fewer than \(3\) of these packets were sold at reduced price.[2]