1) A manager has available a pool of 11 employees who could be assigned to a project-monitoring task. 5 of the employees are women and 6 are men. 3 of the men are brothers. The manager is to make the assignment at random so that each of the

11 employees is equally likely to be chosen. Let A be the event "chosen employee is a man" and B the event "chosen employee is one of the brothers."

a. Find the probability of A.

b. Find the probability of B.

c. Find the probability of the intersection of A and B.

2) A lightbulb manufacturer ships large consignments of lightbulbs to big industrial users. When the production process is functioning correctly, which is 70% of the time, 25% of all bulbs produced are defective. However, the process is susceptible to an occasional malfunction, leading to a defective rate of 50%. If a defective bulb is found, what is the probability that the process is functioning correctly? If a non-defective bulb is found, what is the probability that the process is operating correctly?

a) If a defective bulb is found, the probability that the process is functioning correctly is _____?

b) If a non-defective bulb is found, the probability that the process is functioning correctly is____?