Chapter 5 Review Sheet

Transcription

1 Chapter 5 Review Sheet 1. Which pair of events is disjoint (mutually exclusive)? (a) A = {red cards} B = {face cards} (b) A = {clubs} B = {hearts} (c) A = {spades} B = {black cards} (d) A = {diamonds} B = {threes} 2. If performances on AP Statistics tests are independent and the probability of passing an AP Statistics test is 0.8, then the probability of passing three AP Statistics tests is: (a) 2.4 (b) 0.8 (c) 0.64 (d) (e) % of students at Henry are male. 80% of the females love math, while only 60% of the males love math. What percentage of the student body love math? (a) 70% (b) 50% (c) 71% (d) 60% (e) 100% 4. If 3 coins are tossed, what is the number of equally likely outcomes? (a) 3 (b) 4 (c) 6 (d) 8 (e) 9 5. If P(A) = 0.23 and P(A and B) = 0.12 and P(A or B) = 0.34, find P(B C ). (a) 0.23 (b) 0.52 (c) 0.11 (d) 0.77 (e) How many possible 5-character code words are possible if the first two characters are letters and the last three characters are numbers? Letters and numbers are both chosen without replacement. (a) 468,000 (b) 82 (c) 676,000 (d) 78 (e) Only a math genius can count that high!

2 M.C. Answers: 1-b 2-d 3-c 4-d 5-d 6-a 7. Suppose a person was having two surgeries performed at the same time by different operating teams. The chances of success for surgery A are 85% and the chances of success for surgery B are 90%. Assume that the two surgeries are independent. a) What is the probability that both surgeries are successful? b) What is the probability that surgery A is successful but surgery B fails? c) What is the probability that surgery A or surgery B is successful? d) What is the probability exactly one of the surgeries is successful? 8. In a large city, two newspapers are published. 35% of the homes subscribe to The Post, 30% subscribe to The Gazette, and 15% subscribe to both newspapers. What is the probability a randomly selected home subscribes to (at least) one of the two newspapers?

3 9. Two shipping services offer overnight delivery of parcels, and both promise delivery before 10 a.m. A mail-order catalog company ships 30% of its overnight packages using shipping service 1 and 70% using service 2. Service 1 fails to meet the 10 a.m. delivery promise 10% of the time, whereas service 2 fails to deliver by 10 a.m. 8% of the time. a) Construct a tree diagram having two first-generation branches, for shipped by service 1 and shipped by service 2, and two second-generation branches leading out from each of these, for on time and late. Then provide the probabilities for the diagram. b) What is the probability that a randomly selected package is late? c) What is the probability that a package is shipped by service 2 and is late? d) If a randomly selected package is late, what is the probability that it was shipped by service 2?

4 10. If P(A) = 0.4 and P(B) = 0.3, can we assume that P(A and B) = = 0.12? Explain. 11. Airlines routinely overbook flights because they expect a certain number of noshows. An airline runs a 5 P.M. commuter flight from Washington D.C., to New York City on a plane that holds 38 passengers. Past experience has shown that if 41 tickets are sold for the flight, then the probability distribution for the number who actually show up for the flight is as shown in the table below. Number who actually show up Probability Assume that 41 tickets are sold for each flight. a) There are 38 passenger seats on the flight. What is the probability that all passengers who show up for this flight will get a seat? b) Given that not all passenger seats are filled on a flight, what is the probability that only 36 passengers showed up for the flight? 12. If A B = S, P(A and B C ) = 0.25, and P(A C ) = 0.35, what is P(B)?

5 Chapter 5 Learning Targets: I can explain the difference between trying to predict something in the short run vs. the long run. I can give my own definitions for sample space (S), event, and probability model. I can use the multiplication principle to solve problems. I can explain the difference between sampling with replacement vs. without replacement and how it affects probabilities. I can give the possible values of a probability. I can state the sum of the probabilities for all possible outcomes in the sample space. I can explain what the complement of an event is. I can calculate the probability of the complement of an event. I can calculate probabilities involving or and and. I can define disjoint/mutually exclusive. I can explain what union and intersect are and solve problems involving them. I can explain what it mean for two events to be independent. I can explain the relationship between disjoint events and independent events. I can calculate conditional probabilities. I can make tree-diagrams and use them to calculate conditional probabilities.