4. You work at Rob’s pizza shop. You have the following information about the 7 pizza’s in the oven: 3 of the 7 have thick crust, and of these 1 has only sausage and 2 have only mushrooms; the remaining 4 pizzas have regular crust, and of these 2 have only sausage and 2 have only mushrooms. Choose a pizza at random from the oven.
(a) Are the events {getting a thick crust pizza} and {getting a pizza with mushrooms}independent? Justify your answer with a computation.
(b) You add an eighth pizza to the oven. This pizza has thick crust with only cheese. Now are the events {getting a thick crust pizza}and {getting a pizza with mushrooms} independent? Justify your answer with a computation.
(c) What is the probability of getting a thick crust pizza, given that it has sausage?
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