MTH 232
Section 14.1
The Basics of Probability
Overview
• Probability is the mathematics of uncertainty, in which
the likelihood that a chance event occurs is measured
by a number between 0 (no chance of occurring) and 1
(must certainly occur). Students in grades 3 – 5 should
begin to learn about this measurement.
• Previous to this, students will have begun to describe
events as certain, likely, or impossible.
• Students should explore probability through
experiments that have only a few outcomes (spinners
and dice).
• They should use common fractions to express
probabilities that are neither certain nor impossible.
Important Terms
• Experiment – something that takes place for
which what will happen is uncertain
• Outcome – a possible result
• Sample space – the set of all possible results
• Favorable – what we would like to see happen
• Unfavorable – what we would not like to see
happen
Examples
• For each experiment below, find the sample
space:
1. Rolling a fair die
2. Spinning the spinner shown below
3. Tossing a coin
4. Tossing two coins
Probability Ratio
• The probability that an event E occurs is the
ratio of the number of ways that E can occur
to the number of elements in the sample
space S:
n( E )
Pr( E ) 
n( S )
Examples
• A penny, a nickel, and a dime are tossed. Find
the probability of getting exactly 2 heads.
• A green die and a red die are tossed. Find the
probability that the sum is:
a. 7
b. Less than 4
c. 13
More Examples
• A card is drawn from a standard deck of 52
playing cards. Find the probability that the
card drawn is:
a. Black
b. The queen of diamonds
c. A face card or a club
d. A face card and a club
Yet More Examples
• Recall the age data from our previous class.
a. What is the probability that a randomly
selected person is legal drinking age in the
state of Alabama?
b. What is the probability that a randomly
selected person is over 30, given that the
person is of legal drinking age?
Almost Done
One M&M is chosen at
random.
a. What is the probability that
it is orange?
b. What is the probability that
it is yellow, given that it is a
primary color?
c. What is the probability that
is a primary color, given that
it is yellow?
d. What is the probability that
it is purple?
Modified Homework
• 1 – 10, 14, 16, 32, 34, 35, 36