A restaurant chain is studying the dining habits of its customers. The study finds that half of their customers are women and 25 percent of their women customers are vegetarian. On the other hand, only 15 percent of their male customers are found out to be vegetarian.

a.If a randomly selected customer of the restaurant chain is found out to be a vegetarian, what is the probability that the customer is a woman? Show the necessary work.

b.What is the probability that a randomly selected customer of the restaurant chain will be both a man and a vegetarian? Show the necessary work.

c.What is the probability that a randomly selected customer of the restaurant chain will be either a woman or a vegetarian? Show the necessary work.