Question

When ordering a pizza, I can choose one of three toppings (labeled P, S, V) and one of two kinds of crust (labeled #1 and #2). What is the sample space of the possible outcomes?

Answer 1

{P#1, P#2, S#1, S#2, B#1, B#2}

Explanation:

There are 3 possible options to chose the toppings i.e. P,S and B

There are 2 possible options for crust i.e #1 and #2

Note that for each selected topping I have two options of the crust. For example, if I select topping P, I can select either crust #1 or crust #2. So, my choices will be:

Either P#1 or P#2. Same goes for topping S and B. For topping S, the two possible selections with crust will be:

S#1 and S#2

And for topping B, the options will be:

B#1 and B#2

Sample space is defined as the collection of all possible outcomes. Here, all possible outcomes are all possible combinations of toppings and crust that we just found. So the sample space for this experiment would be:

{P#1, P#2, S#1, S#2, B#1, B#2}

There are total 6 elements in this sample space.