1. Quiz 10-3 You have the following bills in your wallet: three $20’s, four $10’s, five $5’s, and six $1’s. What is the number of distinct ways you could pay out the bills one at a time? 1. 2. How many distinct license plates can be made using 2 digits (numerals 0 – 9) and 4 letters ( a – z) ? 2 digits (numerals 0 – 9) and 4 letters ( a – z) ? # # L L L L # # L L L L 3. What is the probability of getting 4 aces in a randomly dealt hand of 4 cards?

2. 10-4 Disjoint and Overlapping Events

3. Theoretical Probability The probability of an event occurring: There are 4 different colored marbles in a bag (red, blue, green and clear). What is the probability of pulling out a red one and clear). What is the probability of pulling out a red one on the first try? on the first try?

4. Vocabulary compound events: more than one event occurring. picking 2 red AND 1 green. picking 2 red OR1 green. picking 2 red OR 1 green. Is there difference between OR and AND ? Which has the higher probability, OR and AND ? 5 red, 4 blue, 3 green Bag of marbles

5. “Disjoint events: (mutually exclusive). The chance of one event does not affect the chance of another event. “Disjoint events: (mutually exclusive). The chance of one event does not affect the chance of another event. Event #1: picking a red marble from the first bag and Event #2 picking a green marble from the second bag. 4 red, 3 green Bag #2 2 red, 3 green Bag #1

6. “Disjoint events: (mutually exclusive). The chance of one event does not affect the chance of another event. “Disjoint events: (mutually exclusive). The chance of one event does not affect the chance of another event. Event #1: picking a red marble from the bag Event #2 replacing the red marble then picking a green marble from the bag. 2 red, 3 green Bag of marbles

7. “Overlapping events: (not mutually exclusive). The chance of one event is affected by the preceding event. “Overlapping events: (not mutually exclusive). The chance of one event is affected by the preceding event. Event #1: picking a red marble from the bag Event #2 without replacing the red marble, picking a green marble from the bag. 2 red, 3 green Bag of marbles

8. Venn Diagrams Group A Group B Disjoint events: they have nothing in common Disjoint events: they have nothing in common. Elements of group A (only): Number of elements in group A: 4 Elements of group B (only): Number of elements in group B: 2 Total Number of elements in groups A and B: 6

9. Probability of disjoint events. Black Hair RedHair 3 4 “disjoint” (events don’t overlap) P(A or B) = P(A) + P(B)

10. Your turn: There are 20 people in an English class. Five are German, 12 are Mexican, and 3 are Italians. What is the probability of being either Mexican or Italian if you are in this class? 1. 2. What is the probability of dealing either a King or a Queen from a deck of cards if you deal one card only?

11. Venn Diagrams Group B Group A Overlapping events: they have something in common Overlapping events: they have something in common. Elements in group A Elements in group B Elements in group A or B Elements in A: 4 Elements in B: 4 Elements in both A and B: 6 Why can’t you add the number in A and the number in B to get the total number of elements? Double-counting the overlap! Total number = (# in A) + (# in B) – (# in overlap)

12. Probability of overlapping events. BlondeHair Girls Bill Jim Amber Maria Angelica P(blond or Girl) = P(blond) + P(girl) – P(blond and girl) P(A or B)= P(A) + P(B) – P(overlap) P(A or B) = P(A) + P(B) – P(A and B) Total number = (# in A) + (# in B) – (# in overlap)

13. Probability of overlapping events. Hearts Face cards Hearts: J, Q, K total number of cards = ? A, 2,3,4,5,6, 7,8,9,10 Spades: J, Q, K Clubs: J, Q, K Diamonds: J,Q,K # hearts = ? # face cards = ? # hearts and face cards = ? Probability > 1  the universe just “imploded”  the universe just “imploded” = 13 = 22 = 12 = 3 P(A or B) = P(A) + P(B) – P(A and B)

14. Probability of overlapping events. Hearts Face cards Hearts: J, Q, K A, 2,3,4,5,6, 7,8,9,10 Spades: J, Q, K Clubs: J, Q, K Diamonds: J,Q,K What does “OR” mean? “OR”: one of the two conditions is met, NOT BOTH conditions. We need to subtract out the probability of both conditions occurring.

15. Probability of disjoint or overlapping events. “disjoint” (mutually exclusive): “overlapping”

16. Using the formulas: P(A) = 0.5 P(B) = 0.35 “disjoint” (mutually exclusive): “overlapping” P(A and B) = 0.2 P(A or B) = ? P(A) = 0.2 P(B) = 0.6 P(A or B) = 0.7 P(A and B) = ? Solve for P(A and B)

17. Your turn: P(A) = 0.8 P(B) = 0.25 “overlapping” P(A and B) = 0.1 P(A or B) = ? P(A) = 0.37 P(B) = 0.49 P(A or B) = 0.65 P(A and B) = ? Solve for P(A and B) 3. 4.

18. Theoretical Probability The probability of an event occurring: The challenge you have is counting the ways that define success and then counting the total possible outcomes. and then counting the total possible outcomes. What is the probility of pulling an A, followed by a B, and then a C out of a bag with the letters ‘A’, ‘B’, and ‘C’ in it ? a C out of a bag with the letters ‘A’, ‘B’, and ‘C’ in it ?

19. Your Turn: 5. What is the probality of being dealt a 5 card hand that has 3 kings and 2 Aces? 6. What is the probability of picking 1 red or a green marble from a bag containing 2 red and 3 green marbles? 7. In a room of people, there are 15 boys and 17 girls. 5 of the boys have blond hair and 4 or the girls have blond hair. What is the probability of having blond hair? 8. In a room of people, there are 20 boys and 18 girls. 8 of the boys have black hair and 4 or the girls have black hair. What is the probability of not having black hair and being a boy?

20. Geometric Probability 9. What is the probability of hitting the pink ring? 10. What is the probability of hitting either the pink or dark blue ring? 11. What is the probability of not hitting the pink ring?

21. Your Turn: 12. At the Roy High School Talent show 7 musicians are scheduled to perform. They are: Bill, Brad, Bob, and Brody (boys) and Kylee, Kaylee, and Kyla (3 girls). What is the probability that 2 boys will be first?

22. Your Turn: 13. What is the probability of getting 3 aces in a randomly dealt hand of 7 cards?

23. Your Turn: 14. The lottery uses numbers 1 thru 46. 6 numbers are drawn randomly. The order in which you choose the numbers doesn’t matter. What is the probability of winning the lottery if you buy one ticket (assume nobody else picks the winning number) ? How many ways can you get the 6 out of 6 correct numbers? How many ways can you pick 6 of 46 numbers? Is picking 6 of 46 a permutation or a combination?

24. The probability of something NOT happening. The probability that it will rain is 50%. What is the probability that it won’t rain? The probability that it will rain is 20%. What is the probability that it won’t rain? Means: “the probability that event A will not happen.

25. Probability for the Sum of Two Fair Dice Die Roll123456 1234567 2345678 3456789 45678910 567891011 6789101112 Sums Sums

26. Using Venn Diagrams: In a parking lot, 60% of the cars are Fords and the rest are of other makes. 30% of the Fords are white. 50% of all the cars are white. Fords: 0.6 White Cars: 0.5 White Fords 0.18 1.0 - 0.42 - 0.18 – 0.32 = 0.08 What percentage of the cars that are not Fords are not white? Other non-Ford,non-white cars Fords (not white) 0.6*0.7 =0.42 White non- fords: 0.5 – 0.18 =0.32 8% If a car were chosen randomly, what is the probability that it is not a ford and is white? a ford and is white? 32% % of cars that are white fords = 0.3 * 0.6 = 0.18