Probability Concepts → Understanding And Representing Sample Space

1) If a coin is flipped 3 times, how many total outcomes exist?

4

6

8

10

Each flip has 2 possible results, and with three flips the total number of outcomes is 2³ = 8, representing all sequences of heads and tails.

Explanation

Each flip has 2 possible results, and with three flips the total number of outcomes is 2³ = 8, representing all sequences of heads and tails.

2) For a spinner divided into 5 equal parts, how many outcomes are in the sample space?

4

5

6

10

A spinner divided into five equal regions has exactly five possible stopping positions, so the sample space contains one outcome for each labeled section.

Explanation

A spinner divided into five equal regions has exactly five possible stopping positions, so the sample space contains one outcome for each labeled section.

3) Which of the following is not a valid sample space for rolling a die?

{1..6}

{Even,Odd}

{1,2,3,4,5,7}

{Prime,Composite}

A valid sample space must include only outcomes that can actually occur, so listing the number 7 makes the sample space incorrect because a standard die cannot produce that value.

Explanation

A valid sample space must include only outcomes that can actually occur, so listing the number 7 makes the sample space incorrect because a standard die cannot produce that value.

4) True or False: Every event in probability is a subset of the sample space.

True

False

Any event in probability is formed by selecting one or more outcomes from the sample space, so every event must be a subset of the full set of possible results.

Explanation

Any event in probability is formed by selecting one or more outcomes from the sample space, so every event must be a subset of the full set of possible results.

5) A spinner has numbers 1 through 8. What is the probability of landing on an even number?

3/8

1/2

2/8

5/8

Even numbers 2, 4, 6, and 8 account for four out of eight equally likely outcomes, giving a probability of 4/8 = 1/2 and showing how event size compares to total sample space size.

Explanation

Even numbers 2, 4, 6, and 8 account for four out of eight equally likely outcomes, giving a probability of 4/8 = 1/2 and showing how event size compares to total sample space size.

6) If you roll a die, what is the probability of getting a number greater than 4?

1/6

1/3

1/2

2/3

Only the numbers 5 and 6 satisfy the condition “greater than 4,” so the probability is 2 outcomes out of 6, simplifying to 1/3 based on the size of the event relative to the sample space.

Explanation

Only the numbers 5 and 6 satisfy the condition “greater than 4,” so the probability is 2 outcomes out of 6, simplifying to 1/3 based on the size of the event relative to the sample space.

7) A bag contains 5 red, 3 blue, and 2 green balls. What is the sample space for colors?

{Red,Blue,Green}

{1,2,3,4,5}

{5,3,2}

{R,G}

Although the numbers of balls differ, the sample space concerns types of outcomes, so drawing Red, Blue, or Green are the only outcome categories, forming the set {Red, Blue, Green}.

Explanation

Although the numbers of balls differ, the sample space concerns types of outcomes, so drawing Red, Blue, or Green are the only outcome categories, forming the set {Red, Blue, Green}.

8) The total number of possible outcomes in a sample space is called the _______.

The size of a sample space, written n(S), is the count of all distinct outcomes it contains, and it determines how probabilities are computed for any event built from that space.

Explanation

The size of a sample space, written n(S), is the count of all distinct outcomes it contains, and it determines how probabilities are computed for any event built from that space.

Submit

9) What is a sample space in probability?

The set of all possible outcomes of an experiment

The event most likely to happen

The space between two outcomes

The average of all outcomes

A sample space is the complete set of all possible results that can occur in a probability experiment, meaning it must list every outcome such as all faces of a die or both sides of a coin to fully represent the randomness involved.

Explanation

A sample space is the complete set of all possible results that can occur in a probability experiment, meaning it must list every outcome such as all faces of a die or both sides of a coin to fully represent the randomness involved.

10) When you flip one coin, what is the sample space, Heads (H) or Tails (T)?

{H}

{H, T}

{1,2,3,4,5,6}

{H, T, HH, TT}

A single coin flip produces exactly two possible outcomes—Heads or Tails—so the sample space {H, T} accurately lists every result that could occur with equal likelihood.

Explanation

A single coin flip produces exactly two possible outcomes—Heads or Tails—so the sample space {H, T} accurately lists every result that could occur with equal likelihood.

11) Rolling a single six-sided die gives what sample space?

{1,2,3,4,5,6}

{1,2,3}

{Even, Odd}

{1,3,5,7,9}

Rolling a standard die can result in any one of the numbers 1 through 6, so the sample space {1, 2, 3, 4, 5, 6} includes all six possible outcomes.

Explanation

Rolling a standard die can result in any one of the numbers 1 through 6, so the sample space {1, 2, 3, 4, 5, 6} includes all six possible outcomes.

12) If two coins are flipped, how many outcomes are in the sample space?

2

4

3

6

Because each coin has 2 possible results and both flips combine independently, the sample space contains 4 ordered outcomes—HH, HT, TH, TT—giving a total of 4 possibilities.

Explanation

Because each coin has 2 possible results and both flips combine independently, the sample space contains 4 ordered outcomes—HH, HT, TH, TT—giving a total of 4 possibilities.

13) What is the sample space when rolling two dice?

{1,2,3,4,5,6}

{1–12}

All ordered pairs (a,b) with a,b ∈ {1..6}

{2..12}

With each die having 6 sides, the combined experiment produces 36 ordered outcomes written as pairs (a, b), where each number from 1 to 6 can pair with every number from 1 to 6.

Explanation

With each die having 6 sides, the combined experiment produces 36 ordered outcomes written as pairs (a, b), where each number from 1 to 6 can pair with every number from 1 to 6.

14) A spinner has 4 equal sections labeled Red, Blue, Green, Yellow. What is the sample space?

{R,G,B}

{1,2,3,4}

{Red,Blue,Green,Yellow}

{Red,Green,Yellow}

A spinner divided into Red, Blue, Green, and Yellow must list exactly those four color outcomes, forming the sample space {Red, Blue, Green, Yellow}.

Explanation

A spinner divided into Red, Blue, Green, and Yellow must list exactly those four color outcomes, forming the sample space {Red, Blue, Green, Yellow}.

15) If you toss one coin and roll one die, how many outcomes are possible?

8

10

14

12

The experiment has 2 × 6 = 12 possible outcomes because each of the two coin results can pair with each of the six die results, forming 12 distinct combinations.

Explanation

The experiment has 2 × 6 = 12 possible outcomes because each of the two coin results can pair with each of the six die results, forming 12 distinct combinations.

16) Which of the following represents a correct way to show a sample space?

Only as a list

Only as a chart

Only as a table

Any organized method

A sample space can be shown in any organized format—such as a list, a table, or a tree diagram—as long as every possible outcome is clearly included.

Explanation

A sample space can be shown in any organized format—such as a list, a table, or a tree diagram—as long as every possible outcome is clearly included.

17) In the experiment “rolling one die,” how many outcomes are even numbers?

2

3

4

6

The even numbers 2, 4, and 6 form the favorable outcomes, so there are 3 even results in the six-element sample space.

Explanation

The even numbers 2, 4, and 6 form the favorable outcomes, so there are 3 even results in the six-element sample space.

18) A bag has marbles labeled A, B, and C. You pick one marble. What is the sample space?

{A,B,C}

{A,B}

{A,C}

{B,C}

Each marble label represents one possible result of the draw, so the complete sample space is {A, B, C}.

Explanation

Each marble label represents one possible result of the draw, so the complete sample space is {A, B, C}.

19) Which statement about sample spaces is true?

Only list likely outcomes

Include every possible outcome

Depend on experimental results

Contain only favorable outcomes

A sample space must contain every possible outcome of an experiment, not just those that are likely, favorable, or observed, to give a full picture of all possibilities.

Explanation

A sample space must contain every possible outcome of an experiment, not just those that are likely, favorable, or observed, to give a full picture of all possibilities.