MATH II – UNIT 1 PRACTICE TEST – PROBABILITY
OBJECTIVE 1: Students will find the probability of an event using theoretical and experimental methods.
1. Explain the difference between theoretical and experimental probability. Give an example of each.
2. Devon has rolled a four sided die 10 times. Three out of those ten times he has rolled a one. On his next turn, what
is the experimental probability of rolling a one?
3. 250 black or brown dogs were adopted last year from the humane society.
 115 of the dog were female
 165 of the dogs were brown.
 75 were black and male dogs.
What is the probability of randomly choosing a male dog or a brown dog? HINT: make a two way table!!
4. The P(A) = 0.25 and the P(B) = 0.65. If the 𝑃(𝐴 ∪ 𝐵) = 0.23, are these events mutually exclusive? Why or why
not? (Be able to distinguish between independent and mutually exclusive.)
OBJECTIVE 2: Students will find the probability of multiple events using independent and dependent
probability.
5. Explain the difference between independent and dependent probability. Give an example of each.
6. You have an iPod shuffle with 25 with Michael Jackson songs, 32 Miley Cyrus songs, and 15 rap songs. Today
you hit the shuffle button to play songs in a random order. Tomorrow you do the same thing. What is the
probability that you hear Miley Cyrus first each day?
7. In a new board game that recently came out, a player can automatically win the game if they roll a 1 two times in
a row. Amy says that the probability of someone winning this way is ½. Leigh argues that the probability of
someone winning this way is 1/36. Who is correct and WHY?
8. For a carnival game, a jar contains 30 orange marbles and 70 brown marbles.
 Children take turns randomly selecting a marble from the jar.
 If an orange marble is chosen, the child wins a prize.
 After each turn, the marble is replaced.
 Susie has drawn four brown marbles in a row.
Which statement is true?
a. The probability that Susie selects an orange marble on her next turn is higher than it was on her last turn
because she has chosen so many brown marbles.
b. The probability that Susie selects an orange marble on her next turn is the same as it was on her last turn
because selections are independent of each other.
c. If Susie draws 2 more times, she will select 2 orange marbles because the probability that an orange
marble will be selected is 3 out of every 10 turns.
d. If Susie selects another brown marble, then 3 of her next 5 picks will be orange marbles because 3 orange
marbles are selected for every 10 brown marbles selected.
OBJECTIVE 3: Students will read frequency tables and find conditional probability.
A group of people were surveyed about how many pets they own. Use the data recorded in the table
below for # 9-10.
9. If a person was chosen at random out of those who were
surveyed, what is the probability that they would own 1 pet?
10. Find P(2 pets female)?
The UNCC alumni association compiled the following information about its recent graduates.
Use the data below to answer #11-12. Hint: make a tree diagram
• 15% graduated with a B average or better
• 80% of those students who graduated with a B average or better were employed within 6
months of graduation
• 40% of those that graduated with less than a B average were employed within 6 months of
graduation
11. What is the probability that someone is employed within 6 months of graduation AND had an B average?
12. What is the probability that someone had a C average, GIVEN that they are unemployed?
OBJECTIVE 4: Students will use permutations and combinations to solve problems.
13. Moe’s in Charlotte, NC allows customers to design their own burritos. They offer 2 different wraps, 4
different meats, 3 different salsas, 5 different sauces, 3 different cheeses and 8 different vegetables.
They boast that customers can create over 4,000 different burritos if customers pick just one item from
each category! Is this true? How do you know? Show your work to justify your answer.
14. Coach Schmidt is trying to make the best possible batting line-up for next week’s game. How many
different batting orders can he create if he has 10 players?
15. Mrs. Evans’ son is trying to promote his band, Supatight (seriously! Look them up!). He needs to submit
a demo CD to a recording company and isn’t sure what songs to include and in what order. They have
10 new songs, but can only put 3 on the demo CD. How many arrangements of songs are possible?
16. Thirty-five people report for jury duty. How many different 12-person juries can be chosen?
17. Simplify: 2x2 + 3x( 4x – 9) – (3x2- 7x + 1)
18. Multiply (4x – 3)(x + 7)
19. Warren Buffet has offered 1 billion dollars to anyone who submits a perfect NCAA final bracket. If we
start with 64 teams, what is the equation to find the probability of winning?