1. Unit 4 – Combinatorics and Probability Section 4.3 – An Introduction to Probability Calculator Required

2. Probability = compute first number of winnerscompute second Ratios reduce like fractions

3. Independent Dependent Roll a Die Twice Draw two cards with replacement Draw two cards without replacement Choose two letters Repetition allowed Choose two letters Repetition NOT allowed Consistent Denominator For each individual trial Denominator Reduces For each individual trial

4. Find the probability that a four digit number created from the digits 2, 4, 5, 8 is less than 4000. Assume repetition is not allowed. A ball contains three red balls, two blue balls, and one white ball. If two are drawn and replacement is allowed, find the probability that both are red.

5. Two die are rolled. Find the probability that neither is a 5. Independent vs. Dependent Events Rule of Thumb -Do the event twice -On the second time of event, check number of possibilities If the same…..independent…separate fractions If different……dependent…...single fraction…. most likely combinations to be used

6. b. A white or red ball is drawn A single ball is drawn from a bag containing four red, five white and two green balls. Find the probability of each event. a. A red or green ball is drawn

7. In a box there are three red, two blue, and three yellow pastels. Doris randomly selects one, returns it, and then selects another. a. Find the probability that the first pastel is blue and the second pastel is blue b. Find the probability that the first pastel is yellow and the second pastel is red.

8. When Carlos shoots a basketball, the probability that he will make a basket is 0.4. When Brad shoots, the probability of a basket is 0.7. What is the probability that at least one basket is made if Carlos and Brad take one shot each? P(at least one) = 1 – P(none) P(at least one basket) = 1 – P(no baskets) P(Carlos missing) = 0.6P(Brad missing) = 0.3

9. The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event. a. Paula and Leon ask him. b. Ray and Paula ask him, but Leon does not

10. The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event. c. At least two of the three ask him. Leon Yes Paula Yes Ray No Leon Yes Paula No Ray Yes Leon No Paula Yes Ray Yes Leon Yes Paula Yes Ray Yes

11. The probability that Leon will ask Frank to be his tennis partner is ¼, that Paula will ask Frank is 1/3 and that Ray will ask Frank is ¾. Find the probability of each event. d. At least one of the three ask him. P(at least one) = 1 – P(none) P(at least one will ask) = 1 – P(none ask)

12. According to the weather reports, the probability of snow on a certain day is 0.7 in Frankfort and 0.5 in Champaign. Find the probability of each: a. It will snow in Frankfort, but not in Champaign. b. It will snow in both cities. c. It will snow in neither city. d. It will snow in at least one of the cities.

13. State the odds of an event occurring given the probability of the event.

14. From a standard deck of cards, five are drawn. What are the odds of each selection? a. five aces Zero…..there are only four aces in a deck. b. five face cards ODDS 792:2598168 33:108257

15. From a standard deck of cards, five are drawn. What are the odds of each selection? b. five from one suit ODDS 5148:2593812 2574:129691

16. From a standard deck of cards, five are drawn. What are the odds of each selection? b. Two of one suit, three of another