Probability Final Exam Review
NOTE: If it is not stated, assume there is no replacement.
1. How many ways can Four freshmen be chosen from eighteen to be a member of the leadership board?
2. How many ways can Four freshmen be chosen from eighteen to be the Class President, Vice President, Secretary, and
Treasurer?
3. How many ways can you choose five students in a class of twenty to sit in a specific seat?
4. Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways
may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
c) with one of the men and one of the women?
5. There are 10 girls and 10 boys in a class. Four students are to be chosen for a committee. What is the probability that
all four will be girls?
6. United Blood Service says that a person with type O blood and a negative Rh factor. (Rh−) can donate blood to any
person with any blood type.
Find the probability that a person has type O blood or the Rh− factor.



43% of people have type O blood.
15% of people have Rh− factor.
6% of people have both type O and Rh – factor
7. A cell phone company sells 65% of its cell phones with cameras and 40 % of its cell phones with Bluetooth. 30% of
its cell phones have both cameras and Bluetooth.
Find the probability that a cell phone has either a camera or Bluetooth.
8. You have a ten sided number cube. What is the probability of getting a 5 or an odd number?
9. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of
courses have a research paper and a final exam. Find the probability that a course has a final exam or a research
project.
10. In a box of assorted cookies. 36% contain chocolate and 12% contain nuts. Of those, 8% contain both chocolate and
nuts. Find the probability that a cookie contains chocolate or nuts.
11. What is the probability that a card randomly selected from a standard deck will be a king or a club?
12. If a card is drawn from a deck of 52 cards find the probability of choosing a king card and then a black card if the card
is replaced each time?
13. What is the probability of drawing a king and then drawing a queen from a deck of cards when no replacement?
14. If a card is chosen from a stranded deck of 52 cards. Without replacement, another card is chosen. Find the
probability of choosing a black card and then a red card.
15. There is a class with 15 boys and 10 girls. If you are picking two students randomly, what is the probability of
choosing a boy and then a girl?
16. You are dealt five cards. What is the probability that they are all diamonds?
17. At a tire store, 10% of the tires in inventory are defective. If you purchase 4 new tires for your vehicle and they are
randomly selected from the tire inventory, what is the probability that all four will be defective?
18. At a tire store, 10% of the tires in inventory are defective. If you purchase 4 new tires for your vehicle and they are
randomly selected from the tire inventory, what is the probability that at least one will be defective?
19. A box contains 6 white balls and 4 red balls. We randomly (and without replacement) draw three balls from the box.
What is the probability that the third ball will be blue (the only blue drawn)?
20. Three cards are dealt successively at random and without replacement from a standard deck of 52 playing cards. What
is the probability of receiving, in order, a king, a queen, and a jack?
21. A cell phone company sells 65% of its cell phones with cameras and 40 % of its cell phones with Bluetooth. 30% of
its cell phones have both cameras and Bluetooth. Find the probability that a cell phone does not have BOTH a camera
and Bluetooth (only one ore the other).
22. You roll two fair dice: a green one and a red one. What is the probability of getting a sum of 7?
23. In a certain game, the probability of winning is 0.3, and the probability of losing is 0.7. If a player wins, the player
will collect $50. If the player loses, the player will lose $5. What is the expected value of this game? If the game is
played 100 times, what are the expected winnings (or losses) of the player?
24. What is the probability of getting two heads on four flips of a fair coin?
25. In a game of dice, the probability of rolling a 12 is 1/36. The probability of rolling a 9, 10, or 11 is 9/36. The
probability of rolling any other number is 26/36. If the player rolls a 12, the player wins $5. If the player rolls a 9, 10,
or 11, the player wins $1. Otherwise, the player loses $1. What is the expected value of this game? If the game is
played 100 times what are the expected winnings (or losses) of the player?
26. Dennis is in charge of designing a game for the school fund raiser. Participants will be paying $2 for each game.
There will be three prizes. The lowest has a value of $0.50, the second
has
a
value of $1, and
the
first
prize has
an
undetermined value.
The
probability
of winning the lowest
prize is 0.35, the probability of winning the second prize is 0.15, and the
probability
of winning the first
prize
is 0.01. The probability of not winning any prize is 0.49. If the school wants an expected value of $1
per ticket, what should Dennis choose as
the
value of
the
first
prize?
27. A baseball team is having a 10 game homestand. If the probability that they win a game at home is 0.6, find the
probability that they win 7 games on this homestand.
28. The probability of a student graduating from college in four years is 0.4. If 7 students are selected at random, find the
probability that at least 6 of them graduated in four years.
29. Of Colossal Conglomerate's 16,000 clients, 3200 own their own business, 1600 are "gold class" customers, and 800
own their own business and are also "gold class" customers. What is the probability that given a clients owns his or
her own business they are also a "gold class" customer?
30. Suppose that a drug test for an illegal drug is such that it is 98% accurate in the case of a user of that drug (e.g. it
produces a positive result with probability .98 in the case that the tested individual uses the drug) and 90% accurate in
the case of a non-user of the drug (e.g. it is negative with probability .9 in the case the person does not use the drug).
Suppose it is known that 10% of the entire population uses this drug. You test someone and the test is positive. What
is the probability that the tested individual uses this illegal drug?
31. The probability that an egg is cracked is 3%. If you buy two dozen eggs, what is the probability that
a) none of your eggs are cracked
b) at least one of your eggs is cracked
c) exactly two of your eggs are cracked
32. Suppose 5% of cereal boxes contain a prize. You are determined to buy cereal boxes until you win a prize.
a) What is the probability you will have to buy at most 2 boxes?
b) What is the probability you will have to buy exactly 4 boxes?
c) How many boxes to do you expect to buy before you win a prize?
33. The Los Angeles Times (Dec. 13, 1992) reported that 80% of airline passengers prefer to sleep on long flights rather
than watch movies, read, etc. Consider randomly selecting 10 passengers from a particular long flight. Define a
random variable X as preferring to sleep on a plane and answer the following questions.
a)
b)
c)
d)
e)
Calculate and interpret P(X=8)
Calculate and interpret P(X=5)
Calculate and interpret P(x>9)
Calculate the probability that the 5th passenger chosen will be the first one to prefer sleeping.
Calculate the number of passengers you expect to have to select before choosing one that prefers sleeping
ANSWERS
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33.
3060
73440
1860480
A)21 b) 6 c)12
4.33%
52%
75%
50%
86%
40%
30.77%
3.85%
0.60%
25.5%
25%
.05%
0.01%
34.39%
0%
0.05%
45%
16.67%
$11.5 , $1150
37.5% (hint: binary dist)
-$0.33, -$33.33
$265.50
0.18%
0.41%
50%
52.13%
A) 48.14% b) 51.86% c) 0.05%
A) 9.75% b) 4.29% c) 20
A) 30.2% b) 2.642% c) 10.74% d) 0.13% e) 2