1. Lesson 13.1 Find Probabilities and Odds
Essential Question: How do you find the probability of an event?

2. Before we start…
You have a bag of M&M’s that contains: 6 red, 3 orange, 7 yellow, 5 green, 8 blue and 3 brown.
What is the fraction of red M&M’s to total M&M’s?

3. What is an outcome? An outcome is a possible result of an experiment.
Toss a coin: heads or tails.
Pick an M& M: red, orange, yellow, green, blue and brown.

4. What is an event? An event is an outcome or a collection of outcomes.
Rolling an odd number on a dice.
Selecting a primary color M&M.
An event is an outcome or a collection of outcomes.

5. What is a sample space?
A sample space is the set of all possible outcomes.

6. You flip a coin and roll a number cube
You flip a coin and roll a number cube. How many possible outcomes are in the sample space?

7. A bag contains 6 blue cards numbered 1 – 6 and 8 red cards numbered 1 – 8. How many possible outcomes are in the sample space? 1 1

8. You roll two 6-sided number cubes
You roll two 6-sided number cubes. How many possible outcomes are in the sample space?

9. You toss 3 coins. How many possible outcomes are in the sample space?

10. What is probability?
A measure of the likelihood or chance, that the event will occur, ranging from 0 to 1.
Can be expressed as a decimal, fraction or percent.

11. What are the types of probability?
There are two types of probability
Theoretical probability
Experimental probability

12. What is theoretical probability?
Theoretical probability is when all outcomes of an event are equally likely.
The probability of event A is written as P (A)

13. How do you find theoretical probability?
Use the formula:

14. You and your friends designed T-shirts with silk screened emblems, and you are selling the T-shirts to raise money. The table below shows the number of T-shirts you have in each design. A student chooses a T-shirt at random. What is the probability that the student chooses a red T-shirt?

15. A bag contains numbered balls in red, blue, and yellow
A bag contains numbered balls in red, blue, and yellow. The table below shows the numbers of each type of ball. A ball is selected at random. What is the probability that the ball selected is an odd numbered yellow ball?
Red
Blue
Yellow
Even numbered 6 8 10
Odd numbered 11 7

16. A bag contains numbered balls in red, blue, and yellow
A bag contains numbered balls in red, blue, and yellow. The table below shows the numbers of each type of ball. A ball is selected at random. What is the probability that the ball selected is even and red?
Red
Blue
Yellow
Even numbered 6 8 10
Odd numbered 11 7

17. What is the probability that the spinner stops on an odd number?
What is the probability that the spinner stops on an even number?
What is the probability that the spinner stops on a multiple of 3?

18. What is experimental probability?
Is based on the repeated trials of an experiment.
The number of trials is the number of times the experiment is performed.
Each trial in which a favorable outcome occurs is called a success.

19. How do you find experimental probability?
Use the formula:

20. Each section of the spinner shown has the same area
Each section of the spinner shown has the same area. The spinner was spun 20 times. The table shows the results. For which color is the experimental probability of stopping on the color the same as the theoretical probability?

21. You spin the spinner 30 times. It stops on a multiple of 3 five times
You spin the spinner 30 times. It stops on a multiple of 3 five times. What is the experimental probability of stopping on a multiple of 3?

22. Martin has a bag of marbles
Martin has a bag of marbles. He removed one marble, recorded the color and then placed it back in the bag. He repeated this process several times and recorded his results in the table. Find the experimental probability of each color.
Color
Frequency
Red 12
Blue 10
Green 15
Yellow 13

23. Sonja has a bag of ping pong balls
Sonja has a bag of ping pong balls. She removed one ball, recorded the marking and then placed it back in the bag. She repeated this process several times and recorded her results in the table. Find the experimental probability of each marked ping pong ball.
Type
Frequency
Stripes 12
Polka dots 13
Stars 18
Solid color 17
Squares 10

24. What are odds?
The odds of an event compare the number of favorable and unfavorable outcomes when all outcomes are equally likely.
Odds in favor
Odds against

25. How do you find odds?

26. What are the odds in favor of stopping on a multiple of 4?
What are the odds against stopping on a multiple of 6?

27. What are the odds in favor of stopping on 14?
What are the odds against stopping on a multiple of 3?

28. A study indicates that out of every 60 telephone calls, 6 result in busy signals and 12 result in no answer. What are the odds in favor of someone answering? What are the odds against someone answering? What are the odds in favor of a busy signal?

29. Rob buys 9 tickets for a charity raffle. His odds of winning are 3:16
Rob buys 9 tickets for a charity raffle. His odds of winning are 3:16. What is the total number of raffle tickets sold?

30. How do you find the probability of an event?

31. Ticket Out the Door
You roll a six sided number cube. What is the probability of rolling an even number?