Question

When ordering a pizza, you have a choice of 3 types of crust: thin crust (T), hand-tossed (H), or deep dish (D); a choice of 4 types of sauces: red (R), white (W), barbeque (B), or pesto (P); and a choice of 2 types of toppings: mushroom (M) or onions (O). If you are choosing only one of each, list the sample space in regard to the pizzas (combinations of crust, sauces, and toppings) you could pick from.

Answer 1

Definition:

In probability theory, the sample space (also called sample description space or possibility space) of an experiment or random trial is the set of all possible outcomes or results of that experiment

Given:

Number of crust = 3 (T, H, D)

Number of sauces = 4 (R, W, B, P)

Number of toppings = 2 (M, O)

A combination of the crust and sauce gives the following options:

RT , WT, BT, PT, RH, WH, BH, PH, RD, WD, BD and PD

When we include the toppings, we have the following options:

RTM, WTM, BTM, PTM, RHM, WHM, BHM, PHM, RDM, WDM, BDM, PDM, RTO, WTO, BTO, PTO, RHO, WHO, BHO, PHO, RDO, WDO, BDO and PDO

Hence, we have the sample space in regard to the pizza combinations of crust, sauces and toppings is:

RTM, WTM, BTM, PTM, RHM, WHM, BHM, PHM, RDM, WDM, BDM, PDM, RTO, WTO, BTO, PTO, RHO, WHO, BHO, PHO, RDO, WDO, BDO and PDO