Q1:

A factory produces fuses, which are packaged in boxes of 10. Three are fuses selected at random from each box for inspection. The box is rejected if at least one of these three fuses is defective. What is the probability that a box containing five defective fuses will be rejected..

The probability of a box being rejected is the probability that at least one defective fuse is selected for testing. This is the same as 1 minus the probability that no defective fuses are selected for testing. You can get that value using the hypergeometric distribution.

Q2:

An urn contains 24 chips,numbered 1 to 24. One is drawn at random. Let A be the event that the number is divisible by 2 and let B be the event that the number is divisible by 3. Find P(AUB).

I assume they mean divisible by 2 or 3 so that you get an integer. Just go through all the numbers from 1 to 24 and count the number that are “divisible” by 2 or 3 or both and then divide by 24. That’s your answer.

Q3:

In a certain manufacturing process the probability of a type I defect is 0.12 the probability of a type II defect is 0.22 and the probability of having both types of defects is 0.02. Find the probability of having neither type of defect.

All the probabilities have to add to 1. You have values for all the probabilities besides neither type of defect. This should be easy.