TEST 12A (Sec. 12-1, 12-2, 12-3, and 10-2)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
1. A coin is flipped 5 times. How many total possible outcomes are there?
2. A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many
different combinations are possible?
3. There are 6 singers competing at a talent show. In how many different ways can the singers appear if they perform
one at a time?
4. In how many ways can 8 toy animals be arranged in a line on a shelf if one of the toys is a tortoise and it must be at
the end of the line?
5. John is getting his ATM card activated. He must select a password containing 4 nonzero digits to be able to use the
card. How many passwords are allowed if no digit may be used more than once?
6. David’s science quiz has 10 multiple-choice questions. For each question, there are 4 possible answer choices.
How many different choices for answering the 10 questions are possible?
7. For a college debate competition, Daniel must select one topic of six topics to speak at the first level. He must also
select a different topic from the same list to speak at the second level of the competition. How many ways can he
choose the topics for the two levels?
Evaluate the given expression.
8. P(7, 4)
9. C(9, 5)
10. Joel owns 12 shirts and is selecting the ones he will wear to school next week. How many different ways can Joel
choose a group of 5 shirts? (Note that he will not wear the same shirt more than once during the week.)
11. 15 different girls are competing in a track-and-field competition. Assuming that no ties will occur, how many
different ways can a gold, silver, and bronze medal be awarded?
12. How many different ways can the letters in the word GALLAGHER be arranged?
13. In the Super-Ball Lottery, a player must guess which 6 of 50 numbered balls will be selected in a random drawing.
The order that the balls are drawn is not important. How many different choices does a player have in selecting
their 6 numbers?
14. Seven cards are drawn from a standard deck of cards. How many hands consist of 5 hearts and 2 clubs?
15. An experiment consists of spinning a spinner. The table shows the results. Find the experimental probability that
the spinner does not land on red. Express your answer as a fraction in simplest form.
Outcome
red
purple
yellow
Frequency
10
11
13
16. An experiment consists of rolling a number cube. What is the probability of rolling a number greater than 4?
Express your answer as a fraction in simplest form.
17. A person is selected at random. What is the probability that the person was not born on a Monday? Express your
answer as a percent. If necessary, round your answer to the nearest tenth of a percent.
There are 24 children in a class, 16 brown-haired and 8 black-haired. Two students are randomly selected for a
stage performance. Find the probability of the following selection.
18. P(2 brown-haired children)
19. P(2 black-haired children)
20. P(1 brown-haired and 1 black-haired child)
Find the odds of an event occurring with the given the probability of the event.
21.
9
12
Two pens are selected at random from a pen stand containing three blue and two black pens. The table and the
relative-frequency histogram show the distribution of the number of blue pens chosen. Find the probability of each
situation below.
Blue Pens
Probability
0
1
1
3
2
3
10
5
10
22. P(0 blue pens)
23. P(1 blue pen)
24. P(2 black pens)
Write the given equation in logarithmic form.
2
25. 11 = 121
Write the given equation in exponential form.
26. log5 1 = 4
625
Evaluate the logarithmic expression.
27. log2 32
28. Solve the given equation.
log5x  6
29. Solve the given inequality.
log81 b  1
4
Solve the given equation.
30. log5 (x + 2)  log5 3 = log5 9