Name:
Date:
Algebra 2
Probability Review
We will have our end-of-unit test on probability on Friday, June 6. See below for a review outline.
Review Outline

Probabilities in situations where the outcomes are equally likely.
□ Probability of a single outcome =
□ Probability of an event =
1
.
total number of outcomes
number of outcomes in the event
.
total number of outcomes
□ Sometimes counting methods (such as C, P, or !) must be used to find “the total number of
outcomes” and/or “the number of outcomes in the event.”

Probabilities involving “and”, “or”, “not”
□
□
□
□

(here A and B stand for events)
P(not A) = 1 – P(A)
P(A or B) = P(A) + P(B) – P(A and B)
P(A or B) = P(A) + P(B) if A and B are mutually exclusive because then P(A and B) = 0
Problems that can be solved using the last two rules can often also be done with a Venn diagram,
which you may find easier.
Dependent and independent events
□ If events A and B are dependent (the outcome of A affects the likelihood of B):
P(A and B) = P(A) · P(B | A)
where P(B | A) means prob. of B given A
□ If events A and B are independent:
P(A and B) = P(A) · P(B)

Repeated binomial experiments: For an action having two equally-likely outcomes (such as a coin
C
flip) done n times, the probability of getting a certain outcome r-out-of-n times is n n r (get the nCr
2
numbers from a row of Pascal’s triangle).

Expected value (multiply each outcome times its probability, then add)

Conditional probability in tables and tree diagrams
Name:
Date:
Algebra 2
Review Problems
General directions: When asked to find a probability, you may give your answer as a fraction (either
unreduced or reduced) or as a decimal rounded to 3 decimal places.
1. Suppose that the colors of shirts are observed for a random sample of
students. Use the collected data to estimate the following probabilities.
Write your answers first as fractions then as decimals.
a. probability that a student’s shirt is blue
b. probability that a student’s shirt is orange or yellow
color
red
orange
yellow
green
blue
purple
black
white
# of students
24
13
9
25
34
12
31
27
c. probability that a student’s shirt is not black
d. probability that a student’s shirt is neither red nor green
e. probability that if two students are separately chosen (so their probabilities are independent), the
first one’s shirt will be green and the second one’s shirt will be black
f. probability that if two students are separately chosen (so their probabilities are independent), both
will have white shirts
g. Write a question about this situation whose answer is 65/175.
h. Write a question about this situation whose answer is 166/175.
i. Write a question about this situation whose answer is 117/30625.
Name:
Date:
Algebra 2
2. Suppose there are 150 teachers at our school. 38 of them are planning to attend the senior prom, and
97 of them are planning to attend graduation. These numbers include 31 teachers who plan to attend
both events.
Make a Venn diagram of this situation, then answer the probability questions below about a randomly
chosen teacher.
a. probability of attending both events (senior prom and graduation)
b. probability of attending at least one of the events (senior prom or graduation)
c. probability of attending neither of the events
d. Write a question about this situation whose answer is 73/150.
3. Lara and Sara are twins. They have one graphing calculator that they share. Each day they flip a coin
to decide who gets to take the calculator to school. Suppose that they do this for 10 days. Answer
these probability questions about what happens.
a. What is the probability that Sara gets to take the calculator exactly 7 out of the 10 times?
b. What is the probability that Sara gets to take the calculator at least 7 out of the 10 times?
c. Write a question about this situation whose answer is
1
.
1024
Name:
Date:
Algebra 2
4. You have a green die and a red die, each numbered from 1 through 6.
First list all the possible dice rolls. Here’s some space for that:
a. What is the probability of getting a 5 on the green die and a 1 on the red die?
b. What is the probability of getting a 5 and a 1 on the two dice?
c. What is the probability of getting 4’s on both dice?
d. What is the probability that the sum of the two dice is 9?
e. What is the probability that the sum of the two dice is either 7 or 9?
f. What is the probability that the sum of the two dice is not 4?
g. What is the probability that the number on the green die is equal to the number on the red die?
h. What is the probability that the number on the green die is greater than the number on the red die?
Name:
Date:
Algebra 2
5. A cookie jar contains 4 vanilla cookies and 9 chocolate cookies. Once a cookie is taken from the jar, it
is not put back. Suppose that a cookie is randomly taken from the jar, and then a second cookie is
taken from the jar.
a. Make a tree diagram showing the probabilities in this situation.
b. Given that the first cookie is chocolate, what is the probability that the second cookie is vanilla?
c. What is the probability that the first cookie is chocolate and the second cookie is vanilla?
d. What is the probability that the two cookies are of the same kind?
e. What is the probability that the two cookies are of different kinds?
f. Now suppose that five cookies were taken from the jar, one after the other. What is the probability
that all of them are chocolate?
g. Again supposing that five cookies were taken from the jar, what is the probability that all of them
are vanilla?
Name:
Date:
Algebra 2
6. Suppose there’s a lottery game where a player’s ticket shows a row of 4 different capital letters. To
win this lottery, the player has to choose the winning 4 letters in the right order. (For example, if
GBYU is chosen as the winner, then a ticket showing UBYG would not win.) Suppose that a lottery
ticket costs $2, and the prize for winning is $500,000.
a. What is the probability of winning this lottery?
b. What is the expected value of playing this lottery?
7. In a survey of 1000 college students, 60% of the students said they were stressed out by school. Five
percent of the stressed out students dropped out of college before they graduated and two percent of
the non-stressed out students dropped out.
a. Make a table representing this situation.
b. What is the probability that a student drops out of this college?
c. If a student drops out, what is the probability that he or she reported being stressed?
Name:
Date:
Algebra 2
8. Suppose that each year, a driver that’s under age 25 has a 3% probability of having a car accident, and
a driver that’s 25-or-older has a 2% probability of being in a car accident. An insurance company has
20% of its customers under age 25; the rest are 25-or-older. Suppose that one of this company’s
customers has an accident this year. What is the probability that this customer is under age 25?
Hint: Begin by making a table of the situation. Assume the company has a total of 1000 customers.
9. Here is some given information about events X and Y:
□ P(X) = 0.35
□ P(Y | X) = 0.6
□ P(Y | not-X) =
2
3
a. Make a tree diagram where the top-level events are X and not-X; bottom-level events are Y and
not-Y. Label it with probabilities.

b. Find P(X and Y).
Name:
Date:
Algebra 2
10. Here is some probability information about two events S and T:
□ P(S) = 0.6
□ P(S and T) = 0.15
a. Identify something that has a probability of 0.4.
b. Are events S and T mutually exclusive? Justify your answer.
c. If it’s additionally given that S and T are independent, what is P(T) ?
11. Here is the actual data for how many AP classes are being taken by LHS students this year:
number of AP classes
how many students
0
1227
1
408
2
240
3
93
4
12
total students
1980
a. What is the probability that a randomly-chosen LHS student is taking at least one AP class?
b. What is the expected value for the number of AP classes taken by an LHS student?
(In other words, how many AP classes are taken by an LHS student, on average?)
12. From a class which has 14 girls and 6 boys, suppose a group of 3 students is picked. What is the
probability that all 3 students picked are girls? Write your answer first as a fraction then as a decimal.
Name:
Date:
Algebra 2
Answers
1. a. 34/175 b. 22/175 c. 144/175 d. 126/175 e. 775/30625
f. 729/30625
For g/h/i, here’s one possible answer, but there may be others.
g. prob. blue or black h. prob. not yellow i. prob. 1st student orange, 2nd student yellow
2. numbers in the Venn diagram should be 7, 31, 66, 46 (or each of these numbers /150)
a. 31/150 b. 104/150 c. 46/150
d. prob. of attending prom or grad. but not both
C7
120
b. 120+45+10+1=176, answer 176/1024

10
1024
2
c. prob. that Sara takes the calculator all 10 days (OR: none of the 10 days)
3. a.
10
4. a. 1/36
b. 2/36
c. 1/36 d. 4/36
e. 10/36
f. 33/36
g. 6/36
5. a. probabilities should be: 4/13, 9/13; 3/12, 9/12, 4/12, 8/12
15120
b. 4/12 c. 36/156 d. 84/156 e. 72/156 f. 139  128  117  106  95  154440
h. 15/36
g. 0
1
1

358800
26 P4
1
358799
 (2) 
b. 499998 
≈ –0.61.
358800
358800
6. a.
7. a.
Drops out
30
8
38
Stressed
Not stressed
Total
b.
38
1000
c.
Graduates
570
392
962
Total
600
400
1000
30
38
8. Table (assume 1000 drivers)
Accident
Under 25
6
25 or older
16
Totals
22
6
 0.2727
P(under 25 | accident) =
22
No accident
194
784
978
9. a. probabilities should be: 0.35, 0.65; 0.6, 0.4, 2/3, 1/3
b. 0.35 · 0.6 = 0.21
Totals
200
800
1000
Name:
Date:
10. a. P(not S)
Algebra 2
b. No. If they were mutually exclusive, then P(S and T) would be 0.
c. P(S and T) = P(S)  P(T)  0.15 = 0.6  P(T)  P(T) = 0.25.
11. a. 753/1980
b. 0(1227/1980) + 1(408/1980) + 2(240/1980) + 3(93/1980) + 4(12/1980) = 1215/1980  0.614.
12.
C3
 0.319
C
20 3
14