1. Dr. Fowler AFM Unit 7-8 Probability

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4. 4 Classical (or theoretical) probability is used when each outcome in a sample space is equally likely to occur. Classical Probability Example: A die is rolled. Find the probability of Event A: rolling a 5. There is one outcome in Event A: {5} P(A) = “Probability of Event A.” P(Event) = the favorable number of outcomes the number of possible outcomes

5. 5 Empirical (or statistical) probability is based on observations obtained from probability experiments. The empirical frequency of an event E is the relative frequency of event E. Empirical Probability Example: A travel agent determines that in every 50 reservations she makes, 12 will be for a cruise. What is the probability that the next reservation she makes will be for a cruise? P(cruise) =

6. Definition – a probability model will always have: 1) positive values & 2) total values adding up to 1

7. E = All outcomes with 2 Boys & 1 Girl = { BBG, BGB, GBB } = 3 Total Calculate the probability that in a 3 child family there are 2 boys and 1 girl. Assume equally likely outcomes. S = 8 Total outcomes listed

8. 8 Example : You roll a die. Find the probability that you roll a number less than 3 or a 4. The events are mutually exclusive. P (roll a number less than 3 or roll a 4) = P (number is less than 3) + P (4) The Addition Rule – Mutually Exclusive

9. 9 The Addition Rule – Not Mutually Exclusive Example : A card is randomly selected from a deck of cards. Find the probability that the card is a Jack or the card is a heart. The events are not mutually exclusive because the Jack of hearts can occur in both events. P (select a Jack or select a heart) = P (Jack) + P (heart) – P (Jack of hearts)

10. 10 Complementary Events The complement of Event E is the set of all outcomes in the sample space that are not included in event E. (Denoted E′ and read “E prime.”) P(E) + P (E′ ) = 1 Example: There are 5 red chips, 4 blue chips, and 6 white chips in a basket. Find the probability of randomly selecting a chip that is not blue. P(E) = 1 – P (E′ )P (E′ ) = 1 – P(E) P (selecting a blue chip)P (not selecting a blue chip)

11. On the local news the weather reporter stated that the probability of rain tomorrow is 30%. What is the probability that it will not rain?

12. 12 Example : A die is rolled and two coins are tossed. Find the probability of rolling a 5, and flipping two tails. Multiplication Rule P (rolling a 5) = Whether or not the roll is a 5, P (Tail ) = so the events are independent. P (5 and T and T ) = P (5)· P (T )· P (T )

13. Excellent Job !!! Well Done

14. Stop Notes Do Worksheet

15. Introduction to Probability: https://www.youtube.com/watch?v=YWt_u5l_jHs

16. Consider the experiment of drawing a card from a standard 52 card deck of playing cards (ace through king, four suits). Let E represent the event “draw a heart” and let F represent the event “draw an ace”. (b)The word “OR” means Union, so n (E or F) = 16 (all 13 hearts + ace of clubs + ace of diamonds + ace of spades).

17. Consider the experiment of drawing a card from a standard 52 card deck of playing cards (ace through king, four suits). Let E represent the event “draw a heart” and let F represent the event “draw an ace”.

19. Notice – sum of probabilities is 1

21. What is the probability that in a group of 10 people at least 2 people have the same birthday? Assume that there are 365 days in a year.