1. Theoretical Probability
10-4
Theoretical Probability
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Theoretical Probability
Course 2
10-4
Theoretical Probability
Warm Up
1. What is the probability of getting two tails if two coins are tossed?
2. Give the probability that the roll of a number cube will show 1 or 4.
3. Give the expected number of rolls that will result in a 2 if a number cube is rolled 42 times. 1 4 1 3 7

3. Theoretical Probability
Course 2
10-4
Theoretical Probability
Problem of the Day
The name of a U.S. state is spelled out with letter tiles. Then the tiles are placed in a bag, and one is picked at random. What state was spelled out if the probability of picking the letter O is 1 2 ? 3 8 1 3 ? ?
Ohio; Colorado; Oregon

4. Theoretical Probability
Course 2
10-4
Theoretical Probability
Learn to find the theoretical probability of an event.

5. Insert Lesson Title Here
Course 2
10-4
Theoretical Probability
Insert Lesson Title Here
Vocabulary
favorable outcome
theoretical probability
fair

6. Theoretical Probability Theoretical Probability
Course 2
10-4
Theoretical Probability
Theoretical Probability
In the game of Scrabble®, players use tiles bearing the letters of the alphabet to form words. Of the 100 tiles used in a Scrabble game, 12 have the letter E on them. What is the probability of drawing an E from a bag of 100 Scrabble tiles?

7. Theoretical Probability Theoretical Probability
Course 2
10-4
Theoretical Probability
Theoretical Probability
In this case, pulling an E from the bag is called a favorable outcome. A favorable outcome is an outcome that you are looking for when you conduct an experiment.
To find the probability of drawing an E, you can draw tiles from a bag and record your results, or you can find the theoretical probability. Theoretical probability is used to estimate the probability of an event when all the outcomes are equally likely.

8. THEORETICAL PROBABILITY
Course 2
10-4
Theoretical Probability
THEORETICAL PROBABILITY
number of favorable outcomes
probability =
total number of possible outcomes
If each possible outcome of an experiment is equally likely, then the experiment is said to be fair. Experiments involving number cubes and coins are usually assumed to be fair.
You can write probability as a fraction, a decimal, or a percent.

9. Theoretical Probability
Course 2
10-4
Theoretical Probability
Additional Example 1A: Finding Theoretical Probability
Find the probability. Write your answer as a fraction, as a decimal, and as a percent
A. Andy has 20 marbles in a bag. Of these, 9 are clear. What is the probability of drawing a clear marble from the bag?
number of favorable outcomes
total number of possible outcomes
P =
number of clear marbles
total number of marbles
P(clear) =
Write the ratio. = 9 20
Substitute.
Write as a decimal and write as a percent.
= 0.45 = 45%
The theoretical probability of drawing a clear marble is
, 0.45, or 45%. 9 20

10. Theoretical Probability
Course 2
10-4
Theoretical Probability
Additional Example 1B: Finding Theoretical Probability
B. What is the probability of rolling a number less than 4 on a fair number cube.
For a fair number cube, each of the six possible outcomes is equally likely. There are 3 ways to roll a number less than 4: 1, 2, or 3.
P =
number of favorable outcomes
total number of possible outcomes
P(number less than 4) =
3 numbers less than 4
6 possible outcomes = 3 6 1 2 = =
0.5 = 50%
The theoretical probability of rolling a number less than 4 is
0.50, or 50%. 1 2 ,

11. Theoretical Probability
Course 2
10-4
Theoretical Probability
Try This: Example 1A
Find the probability. Write your answer as a fraction, as a decimal, and as a percent.
A. Jane has 20 marbles in a bag. Of these 8 are green.
What is the probability of drawing a green marble
from the bag?
number of favorable outcomes
total number of possible outcomes
P =
number of green marbles
total number of marbles
P(green) =
Write the ratio. = 8 20
Substitute.
Write as a decimal and write as a percent.
= 0.4 = 40%
The theoretical probability of drawing a green marble is
, 0.4, or 40%. 8 20

12. Theoretical Probability
Course 2
10-4
Theoretical Probability
Try This: Example 1B
B. What is the probability of rolling a number more than 4 on a fair number cube.
For a fair number cube, each of the six possible outcomes is equally likely. There are 2 ways to roll a number greater than 4: 5 or 6.
P =
number of favorable outcomes
total number of possible outcomes
P(number more than 4) =
2 numbers more than 4
6 possible outcomes = 2 6 1 3 = 
0.33  33%
The theoretical probability of rolling a number more than 4 is
0.33, or 33%. 1 3 ,

13. Theoretical Probability
Course 2
10-4
Theoretical Probability
Additional Example 2A: School Application
The coach has written the names of each of the track team members on an index card. She draws randomly from these cards to choose a student to run a sprint and then replaces the card in the stack.
A. If there are 13 boys and 10 girls on the team, what is the theoretical probability that a girl’s name will be drawn?
Find the
theoretical
probability.
P(girl) =
number of girls on the team
number of members on the team 10 23
Substitute. =

14. Theoretical Probability
Course 2
10-4
Theoretical Probability
Additional Example 2B: School Application
The coach has written the names of each of the track members on an index card. She draws randomly from these cards to choose a student to run a sprint and then replaces the card in the stack.
B. If there are 13 boys and 10 girls on the team,
what is the theoretical probability that a boy’s name will be drawn?
Find the
theoretical
probability.
P(boy) =
number of boys on the team
number of members on the team 13 23 =
Substitute.

15. Theoretical Probability Insert Lesson Title Here
Course 2
10-4
Theoretical Probability
Insert Lesson Title Here
Try This: Example 2A
A teacher has written the name of each student on a piece of paper and placed the names in a box. She randomly draws a paper from the box to determine which student will present the answer to the problem of the day.
A. If there are 15 boys and 12 girls in the class, what is the theoretical probability that a girl’s name will be drawn?
Find the
theoretical
probability.
P(girl) =
number of girls in the class
number of students in the class 12 27
Substitute. =

16. Theoretical Probability Insert Lesson Title Here
Course 2
10-4
Theoretical Probability
Insert Lesson Title Here
Try This: Example 2B
A teacher has written the name of each student on a piece of paper and placed the names in a box. She randomly draws a paper from the box to determine which student will present the answer to the problem of the day.
B. If there are 15 boys and 12 girls in the class,
what is the theoretical probability that a boy’s name will be drawn?
Find the
theoretical
probability.
P(boy) =
number of boys in the class
number of students in the class 15 27 =
Substitute.

17. Theoretical Probability Insert Lesson Title Here
Course 2
10-4
Theoretical Probability
Insert Lesson Title Here
Lesson Quiz
Find the probabilities. Write your answer as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. You have 11 cards, each with one of the letters from the word mathematics.
1. Find the probability of drawing an m from the pile of shuffled cards.
2. Find the probability of drawing a vowel.
3. Find the probability of drawing a consonant. 2 11
, 0.18, 18% 4 11
, 0.36, 36% 7 11
, 0.64, 64%