Sample Space Answers

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List all the elements of the sample space for the following experiment:You roll a die and toss a penny.

A
(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)
B
(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, H), (2, H), (3, H), (4, H), (5, H), (6, H)
C
(1, T), (2, T), (3, T), (4, T), (5, T), (6, T), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)
D
(1, H), (3, H), (5, H), (2, T), (4, T), (6, T)
3

When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let x be the product of the numbers. Let P be the probability of the desired outcome. Compare the following charts and determine which chart shows the probability distribution for the product of the two numbers. Chart A x 2 3 4 5 6 7 8 9 10 11 12 Px Chart B x 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 Px Chart C x 2 3 4 5 6 8 10 12 15 18 20 24 30 Px Chart D x 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36 Px

Question illustration
A
Chart A
B
Chart B
C
Chart C
D
Chart D
4

List all the elements of the sample space for the following experiment: You spin each of these spinners once.

Question illustration
A
(A, 1), (A, 2), (A, 3), (A, 4), (B, 1), (B, 2), (B, 3), (B, 4)
B
(A, 1), (A, 2), (A, 3), (A, 4), (B, 1), (B, 2), (B, 3), (B, 4), (C, 1), (C, 2), (C, 3), (C, 4), (D, 1), (D, 2), (D, 3), (D, 4)
C
(B, 1), (B, 2), (B, 3), (C, 1), (C, 2), (C, 3)
D
(C, 1), (C, 2), (C, 3), (C, 4), (D, 1), (D, 2), (D, 3), (D, 4), (A, 1), (A, 2), (A, 3), (A, 4)
6

List all the elements of the sample space for the following experiment:You spin a spinner with four equal sections labeled 1, 2, 3, and 4 and toss a dime.

A
(1, H), (2, H), (3, H), (4, H), (1, H), (2, H), (3, H), (4, H)
B
(1, H), (2, H), (3, H), (4, H), (1, T), (2, T), (3, T), (4, T)
C
(1, T), (2, T), (3, T), (4, T), (1, T), (2, T), (3, T), (4, T)
D
(1, H), (H, 1), (2, H), (H, 2), (3, H), (H, 3), (4, H), (H, 4), (1, T), (2, T), (3, T), (4, T)
8

Consider the following experiment: Rolling a die. What is the sample space of the experiment? What is the probability of getting a 1 or a 2?

Question illustration
A
12 possible outcomes; P(1 or 2) =
B
12 possible outcomes; P(1 or 2) =
C
6 possible outcomes; P(1 or 2) =
D
6 possible outcomes; P(1 or 2) =
9

When dealing with the occurrence of more than one event, what multiplication process can be used to easily determine all possible combinations without listing the entire sample space?

A
experiment
B
tree diagram
C
theoretical probability
D
counting principle
10

Examine the following table. x12345P(x)0.20.30.40.10.05Does this table represent a probability distribution? Explain your answer.

A
Yes, because the sum of the probabilites is less than one.
B
Yes, because the sum of the probabilities is more than one.
C
No, because the sum of the probabilities is more than one.
D
No, because the sum of the probabilities is less than one.

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