The pizza below, ordered from the Venn Pizzeria on Bayes Street, is divided into eight slices:

The slices might have pepperoni, mushrooms, olives, and/or anchovies.

Imagine that, late at night, you grab a slice of pizza totally at random (i.e., there is a  chance that you grabbed any one of the eight slices). Base your answers to the following questions on the drawing of the pizza.

a. What is the chance that your slice had pepperoni on it?

b. What is the chance that your slice had both pepperoni and anchovies on it?

c. What is the probability that your slice had either pepperoni or anchovies on it?

d. Are pepperoni and anchovies mutually exclusive on the slices from this pizza?

e. Are olives and mushrooms mutually exclusive on the slices from this pizza?

f. Are getting mushrooms and getting anchovies independent when choosing slices from this pizza?

g. If I pick a slice from this pizza and tell you that it has olives on it, what is the chance that it also has anchovies?

h. If I pick a slice from this pizza and tell you that it has anchovies on it, what is the chance that it also has olives?

i. Seven of your friends each choose a slice at random and eat them without telling you what toppings they had. What is the chance that the last slice left has olives on it?

j. You choose two slices at random from this pizza. What’s the chance that they both have olives on them? (Be careful—after removing the first slice, the probability of choosing one of the remaining slices changes.)

k. What’s the probability that a randomly chosen slice does not have pepperoni on it?

l. Draw a pizza for which mushrooms, olives, anchovies, and pepperoni are all mutually exclusive.

Transcribed Image Text:

Pepperoni Mushroom Olive Anchovy