HW 7 – More Probability
1. (IN CLASS) Homer forgets to set his alarm with a probability of 30%. If he sets the alarm it has an 80% chance of
ringing. If he does not set the alarm it has a 0% chance of ringing. If the alarm rings, he has a 90% chance of making
it to work on time. If the alarm does not ring, he has a 20% chance of making it to work on time. What is the
probability that Homer will make it to work on time tomorrow?
2. (ANSWER GIVEN) An article called “A Puzzling Plague” found in the January 14, 1991 issue of Time stated that
one out of every ten American women will get breast cancer. It also states that of those who do get breast cancer that
one out of four will die of it. Based on this article, what is the probability that an American woman will die of breast
cancer?
3. (SOLUTION GIVEN) Suppose there is a two page written document with one error. Two proofreaders review each
copy. Each has an 80% chance of finding the error. What is the probability the error will be found if:
A) each reads a different page
B) they each read both pages
C) they each pick a page at random to read
4. (HOMEWORK) The probability a certain door is locked is 70%. The key to unlock the door is one of ten keys
hanging on a key rack. You get to pick two keys before walking to the door. What is the probability that you will get
through the door without returning for more keys?
5. (ALTERNATE HW) In sports, championships are often decided by two teams playing each other in a championship
series. Often the fans of the loosing team claim they were unlucky and their team was actually better. Suppose team A
is better and has a 30% chance of loosing in any one game to team B. Suppose a three game series is played, what is
the probability that team A will loose?
6. On a slot machine there are three reels with digits 0, 1, 2, 3, 4, 5, 6 , a bell and a flower. When a coin is inserted and
the level pulled, each of the wheels spins independently and comes to rest on one of the nine positions mentioned. Find
the probabilities:
A) (IN CLASS) only bells and/or flowers appear
B) (ANSWER GIVEN) three flowers appear
C) (SOLUTION GIVEN) exactly one flower and two odd digits appear
D) (HOMEWORK) exactly one flower shows
E) (ALTERNATE HW) exactly two flowers show
7. (IN CLASS) An article in the March 25, 1991 issue of US News and World Reports (pages 69, 70) discussed the use
of clot busters to save the lives of Americans who have heart attacks. The following projections are given:
Treatment
A: current clot buster
B: optimal clot buster
C: optimal clot buster plus prompt medical
use
use
care
Survival
66%
70%
85%
Chance
Suppose these projections are correct and 50% received treatment A, 40% received treatment B, and 10 % received
treatment C.
A) What percent of the individuals survived?
B) If a patient survived what is the probability they received treatment C?
8. (ANSWER GIVEN) For a particular population, 30% are 0-20 years old, 40% are 21-40 years old, and the rest are
over 40. In the 0-20 group 5% have an abnormal glucose test. In the 21-40 group 4% do and in the over 40 group its
10%.
A) What percent have an abnormal glucose test?
B) If a patient has an abnormal glucose test what is the probability they are over 40?
9. (SOLUTION GIVEN) Municipals are rated either A, B or C by a bond rating service. Suppose that 60% were rated
A, 30% B, 10% C. Of the bonds rated A, 40% were from cities, 40% from suburbs, and 20% were rural. Of the bonds
rated B, 50% were from cities, 30% from suburbs, and 20% were rural. Of the bonds rated C, 80% were from cities,
10% from suburbs, and 10% were rural.
A) What percent were rural?
B) Of the rural bonds, what percent were rated C?
10. (HOMEWORK) A company that makes greeting cards has three factories. Factory 1 produces 20% of the cards
while Factory 2 produces 70% and Factory 3 produces 10%. In Factory 1, 12% of the cards are birthday cards. In
factory 2, 20% are birthday cards. In Factory 3, 5% are birthday cards
A) What percent of the cards are birthday cards?
B) If you purchase a birthday card what is the probability that it was made in Factory 3?
9. continued (ALTERNATE HW)
B) What percent were from cities?
C) Of the city bonds, what percent were rated A?
11. (IN CLASS) Suppose that 98% of the buttons produced by Bart’s Button Company are OK. Bart hires an
inspector. The inspector inspects all the buttons and classifies as BAD 90% of the bad buttons, but also accidentally
classifies as BAD 5% of the OK buttons. The buttons classified OK are shipped and those classified BAD are
scrapped.
A) What percentage of the shipped buttons are OK?
B) What percentage of the scrapped buttons are OK?
12. In an article entitled “Why Quitting Means Gaining” in Time magazine it was reported in 1991 that giving up
cigarette smoking often results in gaining weight. In a group of quitters (60% were men and 40% were women), the
following results were found.
Major gain Significant gain Moderate gain Slight gain
Men
9%
14%
22%
55%
Women 12%
11%
27%
50%
A)
B)
C)
D)
(ANSWER GIVEN) If a person had a major gain, what is the probability it was a man?
(SOLUTION GIVEN) If a person had a significant gain, what is the probability it was a woman?
(HOMEWORK) If a person had a moderate gain, what is the probability it was a man?
(ALTERNATE HW) If a person had a slight gain, what is the probability it was a woman?
13. A local baseball team plays 80% of their games at night and 20% during the day. They win 60% of their day
games and 50% of their night games.
A) (IN CLASS) If they won yesterday, what is the probability they played at night?
B) (ANSWER GIVEN) If they lost yesterday, what is the probability they played during the day?
14. (SOLUTION GIVEN) In a group of people, 15% participate in regular aerobic exercise. Of those that do this
exercise, 60% have a cholesterol under 200. Of those that don’t, 20% have a cholesterol under 200. Tim has a
cholesterol under 200, what is the probability he participates in regular aerobic exercise?
15. In a math class it is the case that 60% of the students do all the homework assignments. Of those that do, 90%
pass. Of those that don’t, 55% pass.
A) (HOMEWORK) Lisa passed the class, what is the probability she did all the homework assignments?
B) (ALTERNATE HW) Kristina failed the class, what is the probability she did not do all the homework assignments?