1. Warm Up
1. Two coins are tossed. What is the probability of getting two heads?
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.

2. ANSWERS
Warm Up
1. Two coins are tossed. What is the probability of getting two heads?
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. 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 ? ?

4. ANSWER 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

5. DETERMINE the theoretical probability of an event.
I will…
DETERMINE the theoretical probability of an event.

6. Vocabulary
theoretical probability
equally likely
fair

7. Theoretical probability is used to find the probability of an event when all the outcomes are equally likely.
Equally likely outcomes have the same probability.
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.

8. Example 1a: Finding Theoretical Probability
Andy has 20 marbles in a bag. Of these, 9 are clear and 11 are blue. Find the probability of drawing a clear marble from the bag? Write your answer as a fraction, as a decimal, and as a percent.
number of ways the event can occur
total number of equally likely 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% 9 20
The theoretical probability of drawing a clear marble is
, 0.45, or 45%.

9. Example 1b: Finding Theoretical Probability
Find the probability of drawing a blue marble from the same bag from Example 1a.
number of ways the event can occur
total number of equally likely outcomes
P =
number of blue marbles
total number of marbles
P(blue) =
Write the ratio. = 11 20
Substitute.
Write as a decimal and write as a percent.
= 0.55 = 55%
The theoretical probability of drawing a clear marble is
, 0.55, or 55%. 11 20

10. Write each answer as a fraction, as a decimal, and as a percent.
PRACTICE 1a & 1b
Write each answer as a fraction, as a decimal, and as a percent.
1a.
Jane has 20 marbles in a bag. Of these 8 are green.
Find the probability of drawing a green marble from the bag?
1b.
Find the probability of rolling a number more than 4 on a fair number cube.

11. PRACTICE 1a – WORKED OUT P = P(green) = = = 0.4 = 40%
Jane has 20 marbles in a bag. Of these 8 are green.
Find the probability of drawing a green marble
from the bag? Write your answer as a fraction, as a decimal, and as a percent.
number of ways the event can occur
total number of equally likely 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. PRACTICE 1b – WORKED OUT P = P(number more than 4) = = = =
Find 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 ways the event can occur
total number of equally likely 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. Example 2a: School Application
There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack.
Find the theoretical probability of drawing a boy’s name.
P(boy) =
number of boys on the team
number of members on the team 13 23
P(boy)=
Substitute.

14. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 14 14 14

15. Example 2b: School Application
There are 13 boys and 10 girls on the track team. The name of each of the team members is written on an index card. A card is drawn at random to choose a student to run a sprint and the card is replaced in the stack.
Find the theoretical probability of drawing a girl’s name. 10 23
P(girl) =

16. PRACTICE 2
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.
2a.
If there are 15 boys and 12 girls in the class, what is the theoretical probability that a girl’s name will be drawn?
2b.
What is the theoretical probability that a boy’s name will be drawn?

17. number of girls in the class number of students in the class
PRACTICE 2a – WORKED OUT
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.
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. =

18. PRACTICE 2b – WORKED OUT 12 27 P(girl) + P(boy) = 1 12 27 + P(boy) = 1
What is the theoretical probability that a boy’s name will be drawn?
P(girl) + P(boy) = 1 12 27
Substitute for P(girl). 12 27
+ P(boy) = 1 12 27 12 27
Subtract from both sides 12 27
= - 15 27
Simplify.
P(boy) =

19. 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.

20. 2. Find the probability of drawing a vowel.
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%

21. Lesson Quiz for Student Response Systems
1. A number cube is rolled. Identify the probability of getting a number less than 4 as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D. 21 21 21

22. Lesson Quiz for Student Response Systems
1. A number cube is rolled. Identify the probability of getting a number less than 4 as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D. 22 22 22

23. Lesson Quiz for Student Response Systems
2. There are 40 balls in a bag. Of these 8 are white, 7 are blue, 12 are green, and 13 are yellow. Identify the probability of drawing a white ball as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D. 23 23 23

24. Lesson Quiz for Student Response Systems
2. There are 40 balls in a bag. Of these 8 are white, 7 are blue, 12 are green, and 13 are yellow. Identify the probability of drawing a white ball as a fraction, as a decimal to the nearest hundredth, and as a percent to the nearest whole percent. A. B. C. D. 24 24 24