The number of people who visit a certain store in a day, N, has a Poisson (100) distribution. Ten percent (10%) of the customers are male and 90% are female. Half the men make purchases and only a third of the women make purchases. All shoppers make independent choices to buy something or not. On a particular day, 50 shoppers visit the store but don't buy anything. Given this information, what is the conditional PMF of the number of customers on that day who make a purchase? (Hint: use what you learned about "chicken-egg" questions and define X as the number who buy something, and Y as the number who don't.)

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