Probability
Name _______________________________
Chapter 5 Homework
Read each problem carefully. Write your answer in the blank, or circle the correct answer.
1. Why is the following not a valid probability model?
(circle all that apply)
a) This is not a probability model because P(green) < 0.
b) This is not a probability model because the sum of the
probabilities is not 1.
c) This is not a probability model because P(red) > 0.
d) This is not a probability model because P(brown) > 1.
Color
Red
Green
Blue
Brown
Yellow
Orange
Probability
0.3
–0.2
0.1
0.4
0.2
0.3
2. Describe the sample space of possible outcomes:
Determining an athlete’s sport (Baseball (B), Soccer (S), Football (F))
and skill level (Low (L), Medium (M), High (H))
a)
b)
c)
d)
{BL, BM, SL, SM, FL, FM}
{BL, BM, SL, SM, FL, FM, BL, BM, SL, SM}
{BL, BM, BH, SL, SM, SH, FL, FM, FH, BL, BM, BH}
{BL, BM, BH, SL, SM, SH, FL, FM, FH}
3. Suppose that event S has the following sample space: S = {1, 2, 3, 4}. Suppose all outcomes are
equally likely. Compute P(E) if E = “an odd number less than 4”. Write your answer as a reduced
fraction.
P(E) = _______________
4. A bag of 100 tulip bulbs purchased from a nursery contains 30 red tulip bulbs, 45 yellow tulip bulbs,
and 25 purple tulip bulbs. What is the probability that a randomly selected tulip bulb is yellow?
a)
b)
c)
d)
3
/10
/20
1
/4
3
/2
9
5. In the game of roulette, suppose a wheel has 34 slots numbered 00, 0, 1, 2, 3, 4, …., 32. To play the
game, a metal ball is spun around the wheel and falls into one of the numbered slots. Calculate the
following probabilities. Write answers as reduced fractions.
P(falls into slot 6) = __________
P(falls into an odd slot) = ___________
6. In a national survey, college students were asked, “How often do you wear a seat belt when riding in
a car driven by someone else?” The response frequencies appear in the following table.
Response
Never
Rarely
Sometimes
Most of the time
Always
TOTAL
Frequency
126
326
580
1,334
2,242
Response
Never
Rarely
Sometimes
Most of the time
Always
Probability
4,608
Complete/Construct the probability model above for seat-belt use by a passenger.
Round answers to 3 decimals.
Would you consider it unusual to find a college student who never wears a seat belt when riding in a car
driven by someone else?
a)
b)
c)
d)
No, because there were 126 people in the survey who said they never wear their seat belt.
Yes, because P(never) < 0.05.
No, because the probability of an unusual event is 0.
No, because P(never) > 0.05.
7. Calculate P(Ec) if P(E) = 0.42.
P(Ec) = ___________
8. A golf ball is selected at random from a golf bag. If the golf bag contains 1 black ball, 6 green balls,
and 13 yellow balls, calculate the following probabilities. Write your answers as reduced fractions.
P(golf ball is black or green) = ____________
P(golf ball is not green) = ____________
9. A standard deck of cards contains 52 cards. One card is selected from the deck. Calculate the
following probabilities. Write your answers as reduced fractions.
P(card is a queen or a king) = ____________
P( card is a queen or a king or a three) = ____________
P(card is a king or a diamond) = ____________
10. The data in the following table show the association between cigar smoking and death from cancer
for 133,261 men. Supposed one man is randomly chosen from the group. Calculate the following
probabilities. Round your answers to 4 decimals.
(Note: current cigar smoker means cigar smoker at time of death)
Never Smoked Cigars
Former Cigar Smoker
Current Cigar Smoker
Died from Cancer
870
71
145
Did not die from Cancer
117,594
7,981
6,600
P(died from cancer) = ____________
P(current cigar smoker) = ____________
P(died from cancer and current cigar smoker) = ____________
P(died from cancer or current cigar smoker) = ____________
P(never smoked cigars or did not die from cancer) = ____________
11. The probability that a randomly selected male salamander will live to be 5 years old is 0.64126.
If two male salamanders are randomly selected, what is the probability that both will live to be 5 years
old? (round to 4 decimals)
P(both live to be 5) = ____________
If four male salamanders are randomly selected, what is the probability that all four will live to be 5
years old? (round to 4 decimals)
P(all four live to be 5) = ____________
If four male salamanders are randomly selected, what is the probability that at least one will live to be 5
years old? (round to 4 decimals)
P(at least 1 lives to be 5) = ____________
12. Suppose that a single card is drawn from a standard 52-card deck. Compute the following
probabilities and leave your answers as reduced fractions.
What is the probability that the card drawn is a club?
P(club) = ____________
What is the probability that the card is a club given the card is black?
P(club | black) = ____________
What is the probability that the card is a club given the card is a five?
P(club | five) = ____________
13. A recent poll of 2,278 randomly selected American adults were asked, “When you see an ad
emphasizing that a product is “Made in the USA”, are you more likely to buy it, less likely to buy it,
or neither?” The results of the survey, by age group, are given. Calculate the following probabilities
and round your answers to 4 decimals.
Likelihood
More Likely
Less Likely
Neither
18–34
218
29
298
35–44
385
9
215
45–54
396
27
167
55+
405
15
114
P(55+ | neither) = ____________
P(neither | 55+) = ____________
P(more likely | 18–34) = ____________
14. Suppose that two cards are randomly selected from a standard 52-card deck. Compute the
following probabilities and leave your answers as reduced fractions.
P(first card is a queen, second card is a queen) = ____________
(sampling done WITHOUT replacement)
P(first card is a queen, second card is a queen) = ____________
(sampling done WITH replacement)
15. A woman has eight skirts, ten blouses, and four belts. Assuming that they all match, how many
different skirt-blouse-belt combinations can she wear?
a)
b)
c)
d)
22
320
216
1
16. Suppose Jim is going to burn a CD that will contain 10 songs. How many ways can Jim arrange the
10 songs on the CD?
a)
b)
c)
d)
10
10,000,000,000
3,628,800
100
17. A certain lock has 35 numbers on it. To open it, you turn counterclockwise to a number, then rotate
clockwise to a second number, then counterclockwise to the third number, and so on until a four
number lock combination has been effected. Repetitions are allowed.
How many different lock combinations are there?
a) 1,500,625
b) 1,256,640
c) 140
d) 10,000
What is the probability of guessing the lock combination of the first try? _____________
(write your answer as a fraction)
18. Suppose 16 cars start at a car race. How many ways can the top 3 cars finish the race?
(ie, 1st place, 2nd place, 3rd place)?
a)
b)
c)
d)
48
3,360
560
20,922,789,890,000
19. Four members from a 60-person committee are to be selected randomly to serve as Chairperson,
Vice-Chairperson, Secretary, and Treasurer. How many different leadership structures are possible?
a)
b)
c)
d)
240
11,703,240
487,635
205,320
20. How many samples of size 5 can be obtained from a population whose size is 46?
a)
b)
c)
d)
205,962,976
1,370,754
164,490,480
230