Download Probability Application Set: Name: A poll found that 46% of

Probability Application Set:
Name: _____________________________________________________
1.
A poll found that 46% of Americans suffer great stress at least once a week. If three people are selected at random, find
the probability that all three will say they suffer great stress at least once a week.
2.
A general can plan a campaign to fight one major battle of three small battles. He believes that he has the probability of 0.6
of winning the large battle and a probability of 0.8 of winning each of the small battles. Victories or defeats in the small
battles are independent. The general must win either the large battle or all three small battles to win the campaign. Which
strategy should he choose?
3.
Three cards are drawn from an ordinary deck and not replaced. Find the probability of these events:
a. Getting 3 jacks
4.
b.
Getting an ace, king, and queen in order
c.
Getting a club, spade, and a heart in order
d.
Getting 5 clubs
In each of the following situations, describe a sample space S for the random phenomenon.
a.
A student enrolls in a statistics course and at the end of the semester receives a letter grade [solid grades – no +/-].
b.
A basketball player shoots four free throws. You record the sequence of hits and misses.
c.
A basketball player shoots four free throws. You record the number of baskets made.
5.
Sports writers suggest that the probability of the CHS basketball team winning the division is .65, the probability that they
win the county tournament is .12, and the probability that they win both is .07
a.
What is the probability that the team will either win the division or the county tournament?
b.
What is the probability that the team will not win either of these?
c.
What kind of probability is this based on?
6.
Parking Tickets: The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06, and the probability
that Sam cannot find a legal parking spot and has to park in the no-parking zone is 0.20. On Tuesday, Sam arrives to school
and has to park in a no-parking zone. Find the probability that he will get a parking ticket.
7.
Probability is a measure of how likely an event is to occur. Match each statement about an event with one of the
probabilities that follow: 0
0.01
0.3
0.6
0.99
1
a.
This event is impossible. It can never occur.
b.
This event is certain. It will occur on every trial of the random phenomenon.
c.
This event is very unlikely, but it will occur once in a while in a long sequence of trials.
d.
This event will occur more often than not.
8.
Match each scenario to the correct type of probability:
a. Empirical Probability
Being dealt a pair of kings in a poker game
b. Classical Probability:
Probability of rain on graduation day for CHS
c. Subjective Probability:
Probability of the Yankees beating the Mariners today
9.
The probability of landing on a RED number in roulette is .42 [18/38 = .42] because there are 18 red numbers, 18 black
numbers, and 2 green numbers. Explain in plain language what P(RED) = .42 means. Also, explain why it does NOT mean
that in 38 rolls you will get exactly 18 red numbers.
10. Survey of Women in the Military: A recent survey asked 100 people if they thought women in the armed forces should be
permitted to participate in combat. Here are the results:
Gender
Male
Female
Total
Yes
32
8
40
No
18
42
60
Total
50
50
100
Find these probabilities:
a) The respondent answered yes, given that the respondent was a female:
b) The respondent was a male, given that the respondent answered no.
11. Tossing Coins: A coin is tossed 5 times. Find the probability of getting at least 1 tail.
12. A card is drawn from a deck and replaced; then a second card is drawn. Find the probability of getting a queen and then an
ace.
13. An urn contains 3 red chips, 2 blue chips, and 5 white chips. A chip is selected and its color noted. Then it is replaced. A
second chip is selected and it color noted. Find the probability of each:
a. Selecting 2 blue chips
b.
Selecting 1 blue chip and 1 white chip
c.
Selecting 1 red chip and 1 white chip
14. Approximately 9% of men have a type of color blindness that prevents them from distinguishing between red and green. If
3 men are selected at random, find the probability that all 3 have this type of red-green color blindness.
15. A study showed that 53% of residents in a city had homeowner’s insurance (H) with World Wide Insurance Company. Of
these clients, 27% also had auto insurance (A) with the company. If a resident is selected at random, find the probability
that the resident has both homeowner’s and auto insurance with the company.
16. Select a 1st year college student at random and ask what his or her academic rank was in high school. Here are the
probabilities, based on proportions from a large sample survey of 1 st year students:
Rank
Probability
Top 20%
.41
Second 20%
.23
Third 20%
.29
Fourth 20%
.06
Lowest 20%
.01
a.
What is the sum of these probabilities? Why should the sum have this value?
b.
What is the probability that a randomly chosen 1st year college student was not in the top 20% of his or her high
school?
c.
What is the probability that a 1st year student was in the top 40% in high school?
17. An automobile manufacturer buys computer chips from the supplier. The supplier sends a shipment containing 5%
defective chips. Each chip chosen from this shipment has a probability of 0.05 of being defective, and each automobile uses
12 chips selected independently. What is the probability that all 12 chips in a car will work properly?
18. A string of holiday lights contains 20 lights. The lights are wired in series, so that if any light fails the whole string fails. Each
light has a probability of 0.02 of failing during a 3 year period. The lights fail independently of each other. What is the
probability that the string of lights will remain bright for 3 years?
19. A junk box in your room contains a dozen old batteries, five of which are totally dead. You start picking batteries one at a time
and testing them. Find the probability of each outcome….
(a) The first two you choose are both good.
(b) At least one of the first three batteries you choose works.
(c) The first 4 you pick all work.
(d) You don’t find one that works until the 5th battery.
20. Use the following events and their probabilities for adult males to answer the questions.
Event
Probability
Uses tobacco
.25
Uses tobacco and gets mouth disease
.08
Does not use tobacco and does not get mouth disease
.71
(a) Find the probability that the individual gets mouth disease given that he is a tobacco user.
21. Probability Rules:
a. The probability of an event E must be between _____ and _____.
b.
If an event cannot occur, its probability is _____.
c.
If an event is certain to occur, its probability is _____.
d.
The sum of all probabilities of all outcomes in a sample space is _____.
22. Given: P(A) = .5 and P(B) = .3. Events A and B are independent and not mutually exclusive.
Answer True or False for each statement. If the statement is false, make the correction.
(a) P(A ∩ B) = .15
(b) P(A l B) = .5
(c) P(A ∪ B) = .8
23. Two lie detector tests are used independently on the same individual. The first test has a .9 chance of correctly detecting a lie.
The second has a .7 chance of correctly detecting a lie. If the person taking the test is lying, then…..
(a) What is the probability that both tests will claim he is telling the truth (and thus be wrong)?
(b) What is the probability that at least one of the tests will correctly say the person is lying?
** In the Olympics, athletes are tested for illegal drug use. Suppose that 2% of athletes actually took banned drugs. Suppose further
that if an athlete did take drugs, there is a .5% (.005) chance that the test will be wrong and the test will come out negative. If the
athlete did not take drugs, there is a 1% (.01) chance of a false positive result.
(a) What percent of Olympic athletes will test positive?
(b) What is the probability that an athlete who tests positive actually took the drugs?