Question

You work at Rob’s pizza shop. You have the following informationabout the 7 pizza’s in the oven: 3 of the 7 have thick crust, and ofthese 1 has only sausage and 2 have only mushrooms; the remaining 4pizzas have regular crust, and of these 2 have only sausage and 2 haveonly 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.

Answer 1

Let X = Thick crust and Y = mushrooms.

Probability ( X|Y) = Probability(X)

2/3 ≠ 4/7

Probability (Y|X) = Probability(Y)

1/2 ≠ 3/7

Because the probabilities are not equal, the events are not independent.