3.102 A large corporation organized a ballot for all its workers on a new bonus plan. It was found that 65% of all night-shift workers favored the plan and that 40%

of all female workers favored the plan. Also, 50% of all employees are night-shift workers and 30% of all employees are women. Finally, 20% of all night-shift workers are women.

a. What is the probability that a randomly chosen employee is a woman in favor of the plan?

b. What is the probability that a randomly chosen employee is either a woman or a night-shift worker

(or both)?

c. Is employee gender independent of whether the night shift is worked?

d. What is the probability that a female employee is a night-shift worker?

e. If 50% of all male employees favor the plan, what is the probability that a randomly chosen employee both does not work the night shift and does not favor the plan?