Which Pair of Events Is Disjoint (Mutually Exclusive)?

Ch. 5 Review

1. Which pair of events is disjoint (mutually exclusive)?
2. A = {red cards}B = {face cards}
3. A = {clubs} B = {hearts}
4. A = {spades} B = {black cards}
5. A = {diamonds} B = {threes}

1. Mating eagle pairs typically have two baby eagles (called eaglets). When there are two eaglets, the parents always feed the older eaglet until it has had its fill, and then they feed the younger eaglet. This results in an unequal chance of survival for the two eaglets. Supose that the older eaglet has a 50 percent chance of survival. If the older eaglet survives, the younger eaglet has a 10 percent chance of suvival. If the older eaglet does not survive, the younger eaglet has a 30 percent chance of survival. Let X be the number of eaglets that survive.

Which of the following tables shows the probability distribution of X?

1. A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04 respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

a)Less than 0.01

b)0.078

c)0.080

d)0.922

e)Greater than 0.99

1. The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

a)0.05

b)0.06

c)0.10

d)0.40

e)0.50

1. A sample of 942 homeowners are classified, in the two-way table frequency table below, by the number of credit cards they have and the number of years they have owned their current home.

Of the homeowners in the sample who have four or more credit cards, what proportion have owned their current homes for at least one year?

a)

b)

c)

d)

e)

1. 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.

1. What is the probability that both surgeries are successful?

1. What is the probability that surgery A is successful but surgery B fails?

1. What is the probability that surgery A or surgery B is successful?

1. What is the probability exactly one of the surgeries is successful?

1. 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?

1. If P(A) = 0.4 and P(B) = 0.3, can we assume that P(A and B) = 0.4 • 0.3 = 0.12? Explain.

1. 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.

1. 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.

1. What is the probability that a randomly selected package is late?

1. What is the probability that a package is shipped by service 2 and is late?

1. If a randomly selected package is late, what is the probability that it was shipped by service 2?

10.Every Monday a local radio station gives coupons away to 50 people who correctly answer a question about a news fact from the previous day’s newspaper. The coupons given away are numbered from 1 to 50, with the first person receiving coupon 1, the second person receiving coupon 2, and so on, until all 50 coupons are given away. On the following Saturday, the radio station randomly draws numbers from 1 to 50 and awards cash prizes to the holders of the coupon with these numbers. Numbers continue to be drawn without replacement until the total amount awarded first equals or exceeds $300. If selected, coupons 1 through 5 each have a cash value of $200, coupons 6 through 20 each have a cash value of $100, and coupons 21 through 50 each have a cash value of $50.

a)Explain how you would conduct a simulation using the random table provided below to estimate the distribution of the number of prize winners each week.

b)Perform your simulation 3 times. (That is, run 3 trials of your simulation.) Start at the leftmost digit in the first row of the table and move across. Make your procedure clear so that someone can follow what you did. You must do this by marking directly on or above the table. Report the number of winners in each of your 3 trials

72749133476503026128490670290449953746749461713317

81638365664270933717599431202746547613034669976423

38449464389157901907721460576422400944904983309258

checklist of concepts:

_____describe myths about randomness

_____interpret probability as a long-run relative frequency

_____design and perform simulations, including assigning digits to appropriately model given probabilities, describing the process for using a random digit table or other device to run a trial of a simulation, and calculating the probability estimate after running the simulation

_____define and apply basic rules of probability

_____determine probability from two-way tables and tree diagrams

_____construct Venn Diagrams and determine probabilities

_____use basic probability rules, including the complement rule and the addition rule for mutually exclusive events

_____use the general additional rule to calculate to union of two or more events

_____define and compute conditional probabilities

_____find the probability that events occur using a two-way table and/or tree diagram

_____construct a two-way table and display the data in an appropriate graph

_____represent chance behavior with a tree diagram

_____define independent events

_____determine whether two events are independent

_____apply the general multiplication rule to solve probability questions