Probability Review
1. What is the probability of getting exactly one tail when flipping a coin two times?
2. What is the probability that a family of four children will have all girls?
3. What is the probability that a family of four children will have exactly one girl?
4. There are 6 boys and 3 girls in a room. What is the probability that the two children chosen at
random will be one girl and one boy?
5. Three students are swimming in a race. Todd and Raj each have the same probability of
winning and each is twice as likely to win as Sisco. What is the probability that Todd wins the
race?
6. What is the probability of being dealt five cards, all spades? What is the probability of being
dealt a flush (all cards the same suit)?
7. Three men go to a turkey shoot. Beano has a probability, of hitting the target and winning a
turkey, of 1/6. His cousin Wild Willie has a probability of ¼ and his father-in-law Edge has 1/3
probability of winning. Find the probability that if each man shoots only once that exactly one will
hit the target and win a Thanksgiving Turkey?
8. At Montclair State University, 25% of the boys and 10% of the girls are studying environmental
science. 60% of the students at MSU are girls. Find the probability that, if a student of
environmental science is chosen at random, it is a girl.
9. 20% of the U.S. population has a college degree. What is the probability that of 4 randomly
chosen U.S. citizens, exactly one will have a college degree?
10. Define and write a mathematical expression or:
Disjoint events
Independent events
Mutually exclusive events
Complementary events
11. 6 discs are in a box, 3 are red, 2 are white and 1 is blue. If you were to choose 2 at random w/o
replacement, what would the following probabilities be:
a) The discs are the same color
c) One is red and the other is blue
b) The first is red and the second is blue.
d) The discs are different colors
12. The probability of a random adolescent having a strep throat is .05. The probability that a
throat culture finds strep throat to be strep is .98. A non-strep throat will found to be non-strep
with a probability of .92. What is the probability that if you get a call that your culture was
negative that you in fact do not have strep throat?
13. One thousand students at Illinois State University were classified by GPA and class cutting
habits.
GPA
<2.0 2.0 – 3.0 >3.0
Many cuts 80
25
5
Few cuts
175
450
265
Find the probability that a student has a
a) GPA between 2.0 and 3.0
b) GPA under 2.0 and has a few cuts
c) GPA under 2.0 or has a few cuts
d) GPA under 2.0 given she has many cuts
e) Are GPA and cuts independent?, mutually exclusive?
14. Suppose that in a certain part of the world, in any 50 year period the probability of a major
plague is .39, the probability of a major famine is .52, and the probability of both a plague and a
famine is .15. What is the probability of a famine given that there is a plague?
15. If P(A) = .2 and P(B) = .1, what is P(A U B) if A and B are independent?
16. Approximately 30% of the calls to an airline reservation phone line result in a reservation
being made. What is the probability that at least one call results in a reservation being made?
17. Given the following Venn diagram for the events A, B, and C find these probabilities:
P(A and B)
P(A or C)
P(A|C)
P(Ac ∩ B)
A
.2
.1
.1
.1
.1
.2
B
.1
C
.1