Page 89 - Algebra 1

L E S S O N Determining the Theoretical Probability
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of an Event
Warm Up
1. Vocabulary (Closure, Probability) is the measure of how likely
(Inv 1)
Simplify each expression. 2. 5 × 7 - 27 ÷ 9 + 6
(4)
3. 6.3 + (-2.4) + (-8.9) (10)
4. 6 + ⎪-72⎥ + ⎪-5⎥ (5)
5. Write a number to represent the opposite of “twelve floors up.” (6)
A sample space is the set of all possible outcomes of an event. For example, a toss of a fair coin has two equally likely outcomes. The two possible outcomes, heads and tails, is the sample space.
A simple event is an event having only one outcome. For example, rolling a 5 on a number cube is a simple event.
The theoretical probability of an outcome is found by analyzing a situation in which all outcomes are equally likely, and then finding the ratio of favorable outcomes to all possible outcomes. For example, the probability of tossing a coin and it landing on heads is _1 or 0.5 or 50%.
2
Exploration Finding Theoretical Probability
Place 4 different-colored marbles in a sack. Without looking, draw one marble out of the sack. Record the color in a frequency table.
a. Repeat the experiment 10 times, 20 times, 50 times and 100 times, replacing the marble after each draw.
b. Divide the number of times a red marble is picked by the total number of times you pick a marble. Write this as a probability.
c. Generalize What do you notice about the probabilities as the number of times you pick a marble is increased?
it is that an event will occur.
New Concepts
Math Language
A fair coin has an equally likely chance of landing on heads or tails. The coin is not weighted
so that one outcome is more likely than another.
Color
Tally
Frequency
Red
Green
Yellow
Blue
Materials
· small paper sacks · colored marbles
Online Connection www.SaxonMathResources.com
74 Saxon Algebra 1