MORE PROBABILITY CONCEPTS
 

Properties of Probabilities

Recall that the probability of an event $\,E\,$ is denoted by $\,P(E)\,$.

MULTIPLICATION COUNTING PRINCIPLE
If there are $\,F\,$ choices for how to perform a first act,
and for each of these $\,F\,$ ways,
there are $\,S\,$ choices for how to perform a second act,
then there are $\,F\cdot S\,$ ways to perform the acts in succession.
(The idea extends to more than $\,2\,$ acts.)

The idea is illustrated by the diagram at right.
If there are $\,2\,$ piles, with $\,3\,$ in each pile,
then the total is $\,2\cdot 3 = 6\,$.
EXAMPLE (pizza choices)
Suppose that a pizza shop offers $\,3\,$ types of crust,
$\,2\,$ different types of cheese, and $\,7\,$ different toppings.

A single-topping pizza consists of a choice of crust,
a choice of cheese (if desired), and a choice of topping.

How many different single-topping pizzas are there?
Solution:
There are $\,3\,$ choices for the crust,
$\,3\,$ choices for cheese (none, first type, second type),
and $\,7\,$ choices for the single topping.

By the Multiplication Counting Principle, there are $\,3\cdot 3\cdot 7 = 63\,$ possible single-topping pizzas.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Probability Tree Diagrams


On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5 6 7 8 9 10 11 12 13 14
AVAILABLE MASTERED IN PROGRESS

(MAX is 14; there are 14 different problem types.)