1. CONFIDENTIAL 1 Algebra1 Theoretical Probability

2. CONFIDENTIAL 2 Warm Up 1) choosing a heart. 2) choosing a heart or a diamond. An experiment consists of choosing a card out of a deck and recording the results. Use the table to find the experimental probability of each event. 3) not choosing a club.

3. CONFIDENTIAL 3 Theoretical probability can be used to determine the likelihood of different weather conditions. Theoretical Probability When the outcomes in the sample space of an experiment have the same chance of occurring, the outcomes are said to be equally likely. There is the same chance that the spinner will land on any of the colors. There is a greater chance that the spinner will land on blue than on any other color.

4. CONFIDENTIAL 4 Theoretical Probability theoretical probability = number of ways the event can occur total number of equally likely outcomes An experiment in which all outcomes are equally likely is said to be fair. You can usually assume that experiments involving coins and number cubes are fair. The theoretical probability of an event is the ratio of the number of ways the event can occur to the total number of equally likely outcomes.

5. CONFIDENTIAL 5 Finding Theoretical Probability = 0.1 = 16 2% 3 An experiment consists of rolling a number cube. Find the theoretical probability of each outcome: number of ways the event can occur = 1 total number of equally likely outcomes 6 A) rolling a 3 There is one 3 on a number cube.

6. = 0.5 = 50% An experiment consists of rolling a number cube. Find the theoretical probability of each outcome: number of ways the event can occur = 3 = 1 total number of equally likely outcomes 6 2 B) rolling a number greater than 3 There are 3 numbers greater than 3.

7. CONFIDENTIAL 7 Now you try! 1a) rolling an even number 1b) rolling a multiple of 3 An experiment consists of rolling a number cube. Find the theoretical probability of each outcome:

8. CONFIDENTIAL 8 When you toss a coin, there are two possible outcomes, heads or tails. The table below shows the theoretical probabilities and experimental results of tossing a coin 10 times.

9. CONFIDENTIAL 9 The sum of the probability of heads and the probability of tails is 1, or 100%. This is because it is certain that one of the two outcomes will always occur. P (event happening) + P (event not happening) = 1 The complement of an event is all the outcomes in the sample space that are not included in the event. The sum of the probabilities of an event and its complement is 1, or 100%, because the event will either happen or not happen. P (event) + P (complement of event) = 1

10. CONFIDENTIAL 10 Finding Probability by Using the Complement The weather forecaster predicts a 20% chance of snow. What is the probability that it will not snow? P (snow) + P (not snow) = 100% Either it will snow or it will not snow. 20% + P (not snow) = 100% Subtract 20% from both sides. - 20% 20% P (not snow) = 80%

11. CONFIDENTIAL 11 Now you try! 2) A jar has green, blue, purple, and white marbles. The probability of choosing a green marble is 0.2, the probability of choosing blue is 0.3, the probability of choosing purple is 0.1. What is the probability of choosing white?

12. CONFIDENTIAL 12 Odds ODDS IN FAVOR OF AN EVENT: odds in favor = number of ways the event can occur number of ways an event can fail to happen = a : b Odds are another way to express the likelihood of an event. The odds in favor of an event describe the likelihood that the event will occur. The odds against an event describe the likelihood that the event will not occur. Odds are usually written with a colon in the form a : b, but can also be written as a to b or = a b

13. CONFIDENTIAL 13 ODDS AGAINST AN EVENT: odds against = number of ways an event can fail to happen number of ways the event can occur = b : a a represents the number of ways an event can occur. b represents the number of ways an event can fail to occur. The two numbers given as the odds will add up to the total number of possible outcomes. You can use this relationship to convert between odds and probabilities.

14. CONFIDENTIAL 14 Converting Between Odds and Probabilities Odds in favor = 50 : 50, or 1 : 1 The odds in favor of choosing a red card are 1 : 1. A) The probability of choosing a red card from a standard deck of playing cards is 50%. What are the odds of choosing a red card? The probability of choosing a red card is 50%, so the probability of not drawing a red card is 100% - 50% = 50%.

15. CONFIDENTIAL 15 B) The odds against choosing a green marble from a bag are 5 : 3. What is the probability of choosing a green marble? The odds against green are 5 : 3, so the odds in favor of green are 3 : 5. This means there are 3 favorable outcomes and 5 unfavorable outcomes for a total of 8 possible outcomes. number of ways the event can occur = 3 total possible outcomes 8 The probability of choosing a green marble is = 3 8

16. CONFIDENTIAL 16 Now you try! 3) The odds in favor of winning a free drink are 1 : 24. What is the probability of winning a free drink?

17. CONFIDENTIAL 17 Assessment Find the theoretical probability of each outcome. 1) rolling a number divisible by 3 on a number cube 2) flipping 2 coins and both landing with tails showing 3) randomly choosing the letter S from the letters in STARS 4) rolling a prime number on a number cube

18. CONFIDENTIAL 18 5) A spinner is green, red, and blue. The probability that a spinner will land on green is 15% and red is 35%. What is the probability the spinner will land on blue? 6) The probability of choosing a red marble from a bag is 1/3. What is the probability of not choosing a red marble? 7) The odds against a spinner landing on blue are 3 : 1. What is the probability of the spinner landing on blue?

19. CONFIDENTIAL 19 8) The probability of choosing an ace from a deck of cards is Z 1/13. What are the odds of choosing an ace? 9) The probability of not winning a game is 80%. What are the odds of winning? 10) The odds in favor of a spinner landing on blue are 1 : 3. What is the probability of landing on blue?

20. CONFIDENTIAL 20 Theoretical probability can be used to determine the likelihood of different weather conditions. Theoretical Probability When the outcomes in the sample space of an experiment have the same chance of occurring, the outcomes are said to be equally likely. There is the same chance that the spinner will land on any of the colors. There is a greater chance that the spinner will land on blue than on any other color. Let’s review

21. CONFIDENTIAL 21 Theoretical Probability theoretical probability = number of ways the event can occur total number of equally likely outcomes An experiment in which all outcomes are equally likely is said to be fair. You can usually assume that experiments involving coins and number cubes are fair. The theoretical probability of an event is the ratio of the number of ways the event can occur to the total number of equally likely outcomes.

22. CONFIDENTIAL 22 Finding Theoretical Probability = 0.1 = 16 2% 3 An experiment consists of rolling a number cube. Find the theoretical probability of each outcome: number of ways the event can occur = 1 total number of equally likely outcomes 6 A) rolling a 3 There is one 3 on a number cube.

23. CONFIDENTIAL 23 When you toss a coin, there are two possible outcomes, heads or tails. The table below shows the theoretical probabilities and experimental results of tossing a coin 10 times.

24. CONFIDENTIAL 24 The sum of the probability of heads and the probability of tails is 1, or 100%. This is because it is certain that one of the two outcomes will always occur. P (event happening) + P (event not happening) = 1 The complement of an event is all the outcomes in the sample space that are not included in the event. The sum of the probabilities of an event and its complement is 1, or 100%, because the event will either happen or not happen. P (event) + P (complement of event) = 1

25. CONFIDENTIAL 25 Finding Probability by Using the Complement The weather forecaster predicts a 20% chance of snow. What is the probability that it will not snow? P (snow) + P (not snow) = 100% Either it will snow or it will not snow. 20% + P (not snow) = 100% Subtract 20% from both sides. - 20% 20% P (not snow) = 80%

26. CONFIDENTIAL 26 Odds ODDS IN FAVOR OF AN EVENT: odds in favor = number of ways the event can occur number of ways an event can fail to happen = a : b Odds are another way to express the likelihood of an event. The odds in favor of an event describe the likelihood that the event will occur. The odds against an event describe the likelihood that the event will not occur. Odds are usually written with a colon in the form a : b, but can also be written as a to b or = a b

27. CONFIDENTIAL 27 ODDS AGAINST AN EVENT: odds against = number of ways an event can fail to happen number of ways the event can occur = b : a a represents the number of ways an event can occur. b represents the number of ways an event can fail to occur. The two numbers given as the odds will add up to the total number of possible outcomes. You can use this relationship to convert between odds and probabilities.

28. CONFIDENTIAL 28 You did a great job today!