AnswersConcepts in Probability and Statistics - MA3120 A-ICCompound Events and the Fundamental Counting Principle

Compound Events and the Fundamental Counting Principle Answers

11 verified answers
1
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How many possible outcomes are there when spinning a spinner numbered from 1 to 8 and tossing a coin?

Answer:

16

2
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A sandwich shop offers ham, turkey, tuna, chicken salad, and roast beef. It has Swiss, American, and provolone cheese. You can order a sandwich on white, wheat, or rye bread. If a person orders a sandwich and chooses a meat, cheese, and bread at random, how many sandwich choices are there?

Answer:

45

3

Marcus tosses a coin and spins a spinner numbered from 1 to 3. What is the probability the coin lands heads up and the spinner lands on 1?1/81/61/31/2

A
1/8
B
1/6
C
1/3
D
1/2
4

Janice determined there were 10 possible outcomes when tossing two coins and spinning a spinner numbered 1 through 6. What is the correct number? What might have been Janice’s error?

A
3; There are only 3 events.
B
6; There is only 1 possible outcome for the coins.
C
24; She added the number of possibilities instead of multiplying.
D
36; The spinner was spun twice.
5

3. 81/10,0001/811/416/625

A
81/10,000
B
1/81
C
1/4
D
16/625
6

Tobias’s closet has 1 red hat and 1 black hat; 1 white shirt, 1 black shirt, and 1 black-and-white-striped shirt; and 1 pair of black pants and 1 pair of blue pants. He is picking an outfit by reaching into his closet and randomly choosing a hat, a shirt, and a pair of pants. How many possible outfit combinations are there?

A
3
B
7
C
12
D
16
7

Tobias’s closet has 1 red hat and 1 black hat; 1 white shirt, 1 black shirt, and 1 black-and-white-striped shirt; and 1 pair of black pants and 1 pair of blue pants. He is picking an outfit by reaching into his closet and randomly choosing a hat, a shirt, and a pair of pants. What is the probability he picks an outfit containing only black and/or white colors?1/121/43/43/3

A
1/12
B
1/4
C
3/4
D
3/3
8

A bag contains 5 red, 4 green, and 3 blue marbles. What is the probability of randomly selecting a blue marble, replacing it in the bag, and then randomly selecting a red marble?

A
Option
B
Option
C
Option
D
Option
9

A bag contains 5 red, 4 green, and 3 blue marbles. What is the probability of randomly picking a green marble, replacing it, and then randomly picking a blue marble? 1/125/126/127/12

A
1/12
B
5/12
C
6/12
D
7/12
10

A combination lock has a code consisting of 3 numbers, each of which can be 0 to 39, with numbers repeated. Jillian says that there are only 120 possible codes. Is Jillian correct? If not, explain her error.

Answer:

No, Jillian is not correct. According to the fundamental counting principle, the total number of possible codes would be (40)(40)(40) 64,000. Jillian multiplied by 3 instead of multiplying the number of possibilities for each digit.

11

Check all that you included in your response.

A
The fundamental counting principle says to multiply the number of possibilities for each choice.
B
Jillian multiplied 40 times 3.

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