MORE PROBABILITY CONCEPTS
LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
Thanks for your support!
 

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.)