Q.1. A security analyst feels that the chances are 50% that the price of the shares of a company would increase next week and 20% that price of the share of a company B would rise. The two prices are expected to move independently of each other without any relation with index. Find the probability that in the next week

1. Both prices will rise
2. Only one companys share price will increase
3. Neither of the prices would increase

Q.2. A raw material is supplied to a factory by two vendors A & B. Only 40% of the material received comes from vendor A while the remaining comes from the vendor B. 80% of the lots supplied by A are of exceptional quality while only 50% of the lots supplied by B are of exceptional quality. An incoming shipment of material is inspected and is found to be of exceptional quality. Find, using Bayes theorem, the probabilities that it came from (i) A or (ii) B.

Q.3. A husband and a wife appear in an interview for two vacancies for the same post. The probability of husbands selection is 1/7 and wifes selection is 1/5. A) What is the probability that both of them will be selected? B) What is the probability that only one of the is selected?