1. 0-11: Simple Probability and Odds

2. 0-11: Simple Probability and Odds
Probability: Ratio that compares favorable outcomes to total outcomes
Probability is always between 0 (impossible to occur) and 1 (certain to occur)
Sample Space: The list of all possible outcomes
Equally likely: When there are n outcomes and the probability of each one occurring is 1/n
Example: Rolling a 6-sided die

3. 0-11: Simple Probability and Odds
Example 1: A die is rolled. Find each probability
Rolling a 1 or 5
Two favorable outcomes: 1 and 5
Six possible outcomes: 1, 2, 3, 4, 5, 6
2/6 = 1/3
Rolling an even number
Three favorable outcomes: 2, 4, 6
Six possible outcomes (see above)
3/6 = 1/2

4. 0-11: Simple Probability and Odds
Complements: Opposite events, whose probabilities add up to 1.
Ex: Probability of rolling a 1 and not rolling a 1
Example 2: A bowl contains 5 red chips, 7 blue chips, 6 yellow chips, and 10 green chips. One chip is randomly drawn. Find each probability.
Pulling a blue chip
7/28 = 1/4
Pulling a red or yellow chip
11/28
Not pulling a green chip
Pulling a green chip: 10/28 = 5/14, so…
Not pulling a green chip = 1 – 5/14 = 9/14

5. 0-11: Simple Probability and Odds
Tree diagram: A method used for counting the number of possible outcomes
Example 3: Using a tree diagram
School baseball caps come in blue, yellow, or white. The caps have either the school mascot or the school’s initials. Use a tree diagram to determine the number of different caps possible.
6 outcomes possible
Color
Design
Outcome
Blue
Mascot
Blue, mascot
Initials
Blue, Initials
Yellow
Yellow, Mascot
Yellow, Initials
White
White, Mascot
White, Initials

6. 0-11: Simple Probability and Odds
Fundamental Counting Principle: If an event M can occur in m ways and is followed by an event N that can occur in n ways, then the event M followed by N can occur in m ● n ways
Example: If there are 4 possible sizes for fish tanks and 3 possible shapes, then there are 4 ● 3 = 12 possible fish tanks

7. 0-11: Simple Probability and Odds
Example 4a: Using the fundamental counting principle
An ice cream shop offers one, two, or three scoops of ice cream from among 12 different flavors. The ice cream can be served in a waffle cone, a sugar cone, or in a cup. Use the fundamental counting principle to determine the number of choices
Scoop options: 3
Flavor options: 12
Container options: 3
Total choices: 3 ● 12 ● 3 = 108 different choices of ice cream

8. 0-11: Simple Probability and Odds
Example 4b: Using the fundamental counting principle
Jimmy needs to make a 3-digit password for his log-on name for a website. The password can include any digit from 0-9, but the digits may not repeat. How many possible 3-digit passwords are there?
Options for first digit: 10
Options for second digit: 9
Options for third digit: 8
Total choices: 10 ● 9 ● 8 = 720 different passwords possible

9. 0-11: Simple Probability and Odds
Odds: The ratio that compares the number of ways an event can occur (successes) to the number of ways it cannot occur (failures)
Like fractions, odds get reduced to their simplest form
Ex: The odds of rolling less than a 3 on a number cube
Successes: 2 (1 or 2)
Failures: 4 (3, 4, 5, 6)
The odds are 2:4, or 1:2

10. 0-11: Simple Probability and Odds
Assignment
Page P36
1 – 21 (odds)