You have the following information about 7 pizzas in the oven:3 of 7 pizza are t

Question

You have the following information about 7 pizzas in the oven:3 of 7 pizza are thick crust, and of thse one has only sausage and2 mushroom. the remaining four are regular crust, and of these 2have only sausage and 2 have only mushroom. chooe a pizza at randomfrom the oven. a. are the events (getting a thick crust pizza) and (getting apizzza with mushrooms) independant? explain. b. you add an eighth pizza to the oven. this pizza has thickcrust with only cheese. now are the events (getting a thick crustpizza) and (getting a pizza with mushrooms) independant?explain. You have the following information about 7 pizzas in the oven:3 of 7 pizza are thick crust, and of thse one has only sausage and2 mushroom. the remaining four are regular crust, and of these 2have only sausage and 2 have only mushroom. chooe a pizza at randomfrom the oven. a. are the events (getting a thick crust pizza) and (getting apizzza with mushrooms) independant? explain. b. you add an eighth pizza to the oven. this pizza has thickcrust with only cheese. now are the events (getting a thick crustpizza) and (getting a pizza with mushrooms) independant?explain.

Explanation / Answer

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 toP(thick crust)*P(mushroom) =3/7 * 4/7 Hence the two events are notindependent.
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.(hard to digest !! )
Hope it helps. Feel free to ask for any clarifications

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