Basic Counting Principle Examples

There are 4 different coins in this piggy bank and 6 colors on this spinner.

If you pick 1 coin and spin the spinner:

a) how many possible outcomes could you have?

b) what is the probability that you will pick a quarter and spin a green section?

a) There are 4 different outcomes for the first event (a penny, nickel, dime, or quarter), and 6 different outcomes of the second event. That makes 4 × 6 = 24 different combined outcomes.

b) There is only one way to pick a quarter and spin a green section. So the probability is:

If you spin each of these spinners...

a) how many different combined outcomes could you get?

b) what is the probability that both spinners land on the same color?

a) There are 6 different outcomes on the first spinner, and 4 on the second. The total number of possible combined outcomes is 6 × 4 = 24.

b) These ways give the same color on each spinner: green-green, yellow-yellow, purple-purple, and red-red. That gives us four favorable outcomes.

A pizza parlor allows you to choose between thin or thick crust, whole wheat or plain dough, spicy or regular tomato sauce, and four different types of cheese all before you decide on your toppings.

a) How many different pizzas can you make from these selections?

b) Assuming all options are chosen equally, what is the probability that a thin crust, whole wheat pizza with spicy sauce will be ordered?

a) There are two options for the thickness of the crust, two options for the type of dough, two options for the sauce, and four options for the cheese. This gives a total of 2 × 2 × 2× 4 = 32 different pizzas.

b) Notice that the type of cheese is not specified, so if we list the possible pizzas that have these ingrediants it would be: 

1. thin, whole wheat, spicy, cheese A
2. thin, whole wheat, spicy, cheese B
3. thin, whole wheat, spicy, cheese C
4. thin, whole wheat, spicy, cheese D

That gives 4 favorable pizzas, so the probability is: