You don't like pizza but all your friends love getting pizza so you always go with them and try a new topping and base sauce combination each time until you find a pizza that you like. The probability...

Only need Parts D and E

Extracted text: You don't like pizza but all your friends love getting pizza so you always go with them and try a new topping and base sauce combination each time until you find a pizza that you like. The probability of you liking a pizza is 0.08. The average pizza costs $10 but your friends tell you that if you find a pizza that you like they will give you $80. (a) Let Y be the number of times you try a new pizza before you find one you like. What kind of distribution does Y follow? What would be its expected value and variance? Don't round your answers. (b) You are determined to keep getting pizza until you find one that you like. When you finally find a pizza and your friends give you a congratulatory $80, will you have any profit? What will be the variance of this profit? (c) You only start off with $60. What is the probability that you lose all of your money before you manage to find a pizza that you enjoy? Round your answer to 3 decimal places.


Extracted text: (d) Assume that won a competition and you now have a lifetime supply of pizzas for yourself for free. You go out for pizza 38 times in a year. Let X be the number of times you like your pizza out of the 38 different pizzas that you try. What is the distribution of X? (e) 1) Out of the 38 pizzas that you try, how many would you expect to like? 2) What is the variance of the number of pizzas that you like? Round to 3 decimal places.