Download Notes for Lesson 10-6: Theoretical Probability

Notes for Lesson 10-6: Theoretical Probability
10-6.1 – Finding Theoretical Probability
Vocabulary:
Equally Likely – Having the same probability of occurring
Theoretical Probability – The ratio of the number of equally likely outcomes in an event to the total
number of possible outcomes
Fair – When all outcomes of an experiment are equally likely
When the outcomes in a sample space have the same chance of occurring then we say the outcomes are equally
likely. The roll of a die is an example of equally likely results. However, if the die an 2 ones on it and no 6
then the outcomes would not be equally likely because the one would have a greater probability since it occurs
twice.
In 10-5 we talked about how experimental probability is based on what has happened as a result of an
experiment taking place. Theoretical probability is the probability that something should happen based on
outcomes all being equally likely.
favorable outcomes
Total outcomes
Examples: Find the theoretical probability of each event.
Theoretical probability can be found by
Rolling a 3 on a die:
1
6
3 1
or
6 2
13 1
Picking a heart from a deck of cards:

52 4
Rolling a number greater than 3:
10-6.2 – Finding Probability by using the complement
Vocabulary:
Complement – All outcomes in the sample space that are not in event A
The complement is everything that you do not want. The sum of the probability and its complement is always
1. For example, if there is a 25% chance of drawing a spade from a deck of cards, then there is a 75% chance
you will not draw a spade from the deck.
Examples:
The weather forecaster predicts a 20% chance of rain. What is the probability it will not rain?
100 – 20 = 80
80% chance it will not rain
3
, what is the probability of not drawing a red marble?
4
¼ chance of not drawing a red marble.
The probability of choosing a red marble is
1–¾=¼
10-6.3 – Converting between odds and probabilities
Vocabulary:
Odds – A comparison of favorable and unfavorable outcomes.
Odds are shown as a ratio of good results to bad result. The two numbers given in the odds will add up to the
total number of outcomes.
If the odds of spinning a 4 on a spinner is 1:3, What is the probability of spinning a 4?
other than a 4?
1
Spinning anything
4
3
4
Examples: The odds the choosing a green marble from a bag are 5:3. What is the probability of choosing a
5
green marble?
8
Do Practice B #’s 1-12