The manager of a movie theatre wishes to study the relationship between the gender of a guest and whether the guest purchases popcorn. To investigate the relationship between the manager collected the following information on 200 recent customers:

Purchased	Male	Female	Total
Yes	93	32	125
No	18	57	75
	111	89	200

(a) Draw a probability tree diagram showing all possible outcomes (sample space), conditional probabilities, and joint probabilities. Round all probabilities to 3 decimal places if required. (b) Show that all the joint probabilities total to 1.000 (c) If one guest was selected at random, what is the probability the selection would be a female that did not purchase popcorn? Give your answer as a percent number to one decimal place. (d) If one trainee was selected at random, what is the probability the selection would be a male that did purchase popcorn? Give your answer as a percent number to one decimal place.