13.37 Thomas\'s pizza. You work at Thomas\'s pizza she You have the following in

Question

13.37 Thomas's pizza. You work at Thomas's pizza she You have the following information about the seven pizzas in the oven: three of the seven have thick crust, and of these one has only sausage and two have only mushrooms; the remaining four pizzas have regular crust, and of these two have only sau- sage and two have only mushrooms. Choose a pizza at random from the oven. (a) Are the events "getting a thick crust pizza" and "get- ting a pizza with mushrooms" independent? Explain. (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? Explain. A probability teaser. Suppose (as is roughly correct) 13.38

Explanation / Answer

Solution:

(a)

In all there are 7 pizzas and they are :

1 sausage thick crust, 2 mushroom thick crust, 2 sausageregular, 2 sausage mushroom

P(thick crust) = 3/7

P(regular) = 4/7

P(sausage)=3/7

P(mushroom)=4/7

P(thick crust and mushroom) = 2/7 which is not equivalent to P(thick crust)*P(mushroom) = 3/7 * 4/7

Hence the two events are not independent.

(b)

Now if we add one more pizza

P(thick crust with mushroom) 2/8 =1/4

P(thich crust)*P(mushroom) = 4/8 * 4/8 = 1/4 .

Hence P(A B) =P(A)*P(B) is satisfied. Though theydon't seem to be independent they are statistically independent.

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