Download Ch. 5 Review Which pair of events is disjoint (mutually exclusive)? A

Ch. 5 Review
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. 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?
3. 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)
b)
c)
d)
e)
Less than 0.01
0.078
0.080
0.922
Greater than 0.99
4. 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)
b)
c)
d)
e)
0.05
0.06
0.10
0.40
0.50
5. 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?
78
a) 212
b)
c)
78
258
78
942
d)
212
e)
258
942
942
6. 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?
7. 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?
8. 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.
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 secondgeneration 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?
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
72749 13347 65030 26128 49067 02904 49953 74674 94617 13317
81638 36566 42709 33717 59943 12027 46547 61303 46699 76423
38449 46438 91579 01907 72146 05764 22400 94490 49833 09258
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