Practice Test 5
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Jan 9, 2024
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Algebra 2B | Unit 5 Practice Test | Counting and Probability
Name: _______________________________________
Unit 5 Practice Test This extra credit practice test is worth 10 points. You MUST
do the following to earn the points:
Print out the practice test and write directly on the paper (you may use snipping tool).
Show work for each problem. If there is no work to show, explain your answer.
1)
When ordering a pizza, I can choose one of three toppings (labeled P, S, V) and one of
two kinds of crust (labeled #1 and #2). What is the sample space of the possible
outcomes?
PT ST MT 3 x 2 = 6
PP SP MP
2)
I’m taking a walk and at each corner I will choose one of the 4 cardinal directions (N, S,
E, W) to walk. If I choose at random three different times, how many possible outcomes
are there?
4 x 4 x 4 = 64
3)
There are two spinners. The first spinner has three equal sectors labeled 1, 2, and 3. The
second spinner has four equal sectors labeled 3, 4, 5, and 6. Each spinner is spun once.
How many outcomes do not
show an even number on the first spinner and show an odd
number on the second spinner?
13, 14, 15, 16 4 outcomes
23, 24, 25, 26
33, 34, 35, 36
Algebra 2B | Unit 5 Practice Test | Counting and Probability
Algebra 2B | Unit 5 Practice Test | Counting and Probability
4)
Which events are independent? Select all correct answers.
A) A coin is flipped three times in a row
B) 10 cards are drawn out of a deck without replacement
C) A die is rolled while a spinner is spun
D) 5 marbles are drawn out of a bag, being replaced each time
5)
Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not
replaced before selecting the second slip of paper. What is the probability of selecting an
even number and then selecting an odd number greater than 2?
1 2 3 4 5 6 7 8 9 10
5/10 x 4/9 = 20/90 = 2/9
6)
There are 4 green marbles, 6 blue marbles, and 2 yellow marbles in a jar. One marble is
randomly drawn and replaced before a second marble is drawn. What is the probability
of drawing a blue marble and then a yellow marble?
6/12 x 2/12 = 12/144 = 1/12
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Algebra 2B | Unit 5 Practice Test | Counting and Probability
7)
A and B are two events. Given that P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.02. Choose the correct answers to fill in the blanks.
Events A and B are INDEPENDENT
or NOT INDEPENDENT
because _____________ P(A|B) = P(A)
P(A|B) = P(B)
P(A|B) ≠ P(A)
8)
A group of people were asked if they like coffee or tea. The table shows the probabilities
of the results.
Like tea
Do not like tea
Total
Like coffee
0.25
0.5
0.75
Do not like coffee
0.1
0.15
0.25
Total
0.35
0.65
1
(continued on next page)
Which statement is true? A) Liking coffee and tea are not independent because P(coffee|tea) = P(coffee).
B) Liking coffee and tea are independent because P(coffee|tea) = P(coffee).
C) Liking coffee and tea are not independent since P(coffee|tea) ≠ P(coffee) and P(tea|coffee) ≠
P(tea).
D) Liking coffee and tea are independent since P(coffee|tea) ≠ P(coffee) and P(tea|coffee) ≠
P(tea).
Algebra 2B | Unit 5 Practice Test | Counting and Probability
9)
Explain the difference between P(A|B) and P(A) and P(B) given that events A and B are
independent events.
For independent A and B, P(A|B) = P(A)
Conditional probability is P(A|B) = P(A&B)/P(B)
When A and B are independent P(A&B) = P(A)·P(B)
Then, the conditional probability is P(A|B) = (P(A)·P(B))/P(B) = P(A) for independent A and B
When A and B are independent, the probability of A given B is the same as the probability of A. That means that the probability of B has no effect on the probability of A.
10)
The probability of drawing two red marbles without replacement is 1
7
, and the
probability of drawing one red marble is 2
5
.What is the probability of drawing a second
red marble, given that the first marble is red?
2/5 x P = 1/7
P = 1/7 x 5/2 =5/14
11)
A 12-sided die is rolled. What is the probability of getting a multiple of 3 or a
number less than 4?
Multiple of 3 from #1-12: 3, 6, 9, 12
Less than 4 from #1-12: 1, 2, 3
Multiple of 3 and less than 4 from #1-12: 1, 2, 3, 6, 9, 12
P = 6/12 = 1/2
12)
A spinner has fifteen equal sectors labeled from 1 to 15. The spinner is spun once.
What is the probability of getting an even number or a multiple of 5?
Algebra 2B | Unit 5 Practice Test | Counting and Probability
Even number from #1-15: 2, 4, 6, 8, 10, 12, 14
Multiple of 5 from #1-15: 5, 10, 15
Even number or multiple of 5 from #1-15: 2, 4, 5, 6, 8, 10, 12, 14, 15
P = 9/15 = 3/5
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