Identifying Outcomes In A Sample Space Quiz

1) A jar has letter tiles: A, A, B, C. One tile is drawn at random. Which sample space and counts are correct?

{A, A, B, C} with A more likely than B or C

{A, B, C} with all equally likely

{A, B, C} with A less likely

{A, B, C} with C more likely

There are four tiles total, and A appears twice.

Since A is in the set two times, you are twice as likely to draw A compared to B or C.

Therefore, the sample space must include A twice.

Explanation

There are four tiles total, and A appears twice.

Since A is in the set two times, you are twice as likely to draw A compared to B or C.

Therefore, the sample space must include A twice.

2) A game board spinner has 8 equal spaces numbered 1–8. Which is a correct description of an outcome and its likelihood?

Spinning a 9 is unlikely

Spinning an even number is impossible

Spinning a number from 1 to 8 is possible, and each single number is equally likely

Spinning a 1 is certain

The spinner can only land on numbers 1–8, and they are equally spaced.

So each number is equally likely, and spinning a number outside the range is impossible.

Explanation

The spinner can only land on numbers 1–8, and they are equally spaced.

So each number is equally likely, and spinning a number outside the range is impossible.

3) You flip a fair coin twice. Which sample space lists all possible ordered outcomes?

H, T

HH, HT, TH, TT

HH, TT

HHT, TTH

Each flip has 2 outcomes.

Two flips produce four ordered outcomes:

both heads

head then tail

tail then head

both tails

These cover all possibilities.

Explanation

Each flip has 2 outcomes.

Two flips produce four ordered outcomes:

both heads

head then tail

tail then head

both tails

These cover all possibilities.

4) A bag has 4 green, 4 yellow, and 4 purple beads. One bead is chosen at random. Which statement is true?

Green is more likely than yellow.

Purple is less likely than green.

Yellow is impossible.

All colors are equally likely.

Each color appears 4 times, so no color is more or less likely.

They have equal probability.

Explanation

Each color appears 4 times, so no color is more or less likely.

They have equal probability.

5) Which list shows all outcomes when choosing a day from a school week?

Monday, Tuesday, Wednesday, Thursday, Friday

Monday, Tuesday, Wednesday, Thursday

Monday, Wednesday, Friday

Monday, Tuesday, Thursday, Friday, Saturday

A school week includes five weekdays.

Saturday is not part of the school week, and option A lists all correct days

Explanation

A school week includes five weekdays.

Saturday is not part of the school week, and option A lists all correct days

6) A number is chosen at random from the set {2, 4, 6, 8}. Which statement is true?

Odd is possible.

Prime is certain.

Odd is impossible.

2 is impossible.

All numbers in the set are even, so it is impossible to choose an odd number.

Explanation

All numbers in the set are even, so it is impossible to choose an odd number.

7) A spinner has 3 equal sections labeled Cat, Dog, Bird. Which outcome is impossible?

Cat

Dog

Bird

Fish

Fish is not on the spinner, so that outcome cannot happen.

Explanation

Fish is not on the spinner, so that outcome cannot happen.

8) For two fair number cubes, which of the following is a correct set of possible sums?

1, 2, 3, …, 12

2, 3, 4, …, 12

0, 1, 2, …, 12

3, 4, 5, …, 12

The smallest sum is 1+1 = 2.

The largest sum is 6+6 = 12.

All sums between 2 and 12 are possible; sums outside this range cannot occur.

Explanation

The smallest sum is 1+1 = 2.

The largest sum is 6+6 = 12.

All sums between 2 and 12 are possible; sums outside this range cannot occur.

9) You roll two fair number cubes. Which is the correct sample space size (number of outcomes)?

6

36

12

72

Each die has 6 outcomes.

Two dice rolled together give 6 × 6 = 36 different ordered pairs.

This represents every unique combination of the two rolls.

Explanation

Each die has 6 outcomes.

Two dice rolled together give 6 × 6 = 36 different ordered pairs.

This represents every unique combination of the two rolls.

10) A spinner has 5 equal sections labeled 1, 2, 3, 4, 5. Which statement is true?

Each outcome is equally likely.

1 is more likely than 4.

3 is impossible.

5 is certain.

All 5 sections are the same size, so each number has an equal probability of being spun.

No number is more or less likely than another.

Explanation

All 5 sections are the same size, so each number has an equal probability of being spun.

No number is more or less likely than another.

11) Which of the following lists represents the complete sample space for spinning the spinner once and rolling the number cube once (as ordered pairs Spinner, Die)?

(R, 1), (B, 2), (G, 3), (Y, 4), (R, 5), (B, 6)

(R, 1), (R, 2), (R, 3), (R, 4), (R, 5), (R, 6)

(R, 1), (B, 1), (G, 1), (Y, 1)

The spinner has 4 possible outcomes (R, B, G, Y).

The die has 6 possible outcomes (1–6).

To list the complete sample space, we must pair each color with every number.

That creates 4 × 6 = 24 ordered pairs, which option D shows.

The other options leave out many combinations, so they are incomplete.

Explanation

The spinner has 4 possible outcomes (R, B, G, Y).

The die has 6 possible outcomes (1–6).

To list the complete sample space, we must pair each color with every number.

That creates 4 × 6 = 24 ordered pairs, which option D shows.

The other options leave out many combinations, so they are incomplete.

12) Which list correctly shows all outcomes for rolling a fair number cube?

0, 1, 2, 3, 4, 5

1, 2, 3, 4, 5, 6

1, 2, 3, 4, 5

1, 2, 3, 4, 5, 6, 7

A number cube (die) has six faces labelled with numbers 1 through 6.

No other numbers are possible.

Explanation

A number cube (die) has six faces labelled with numbers 1 through 6.

No other numbers are possible.

13) A fair coin is flipped and a fair 3-sided spinner labeled 1, 2, 3 is spun. Which statement is true?

The sample space has 3 outcomes.

The sample space has 8 outcomes.

The sample space has 6 outcomes.

The sample space has 12 outcomes.

A coin has 2 outcomes (H, T).

The spinner has 3 outcomes (1, 2, 3).

Multiplying: 2 × 3 = 6 possible combinations.

Explanation

A coin has 2 outcomes (H, T).

The spinner has 3 outcomes (1, 2, 3).

Multiplying: 2 × 3 = 6 possible combinations.

14) A bag contains 3 red marbles and 2 blue marbles. One marble is drawn. Which outcome is impossible?

Red

Blue

Green

Drawing any one marble

The bag contains only red and blue marbles.

Since green is not in the bag, drawing a green marble cannot happen.

Explanation

The bag contains only red and blue marbles.

Since green is not in the bag, drawing a green marble cannot happen.

15) A standard deck is reduced to these 8 cards: A, 2, 3, 4 of Hearts and A, 2, 3, 4 of Spades. If one card is drawn at random, which is the correct sample space?

{A♥, 2♥, 3♥, 4♥, A♠, 2♠, 3♠, 4♠}

{A♥, 2♥, 3♥, 4♥}

{Hearts, Spades}

{A, 2, 3, 4}

The deck includes A, 2, 3, 4 in two suits: Hearts and Spades.

The sample space must list all 8 individual cards, not just values or suits.

Option A is the only list that does this correctly.

Explanation

The deck includes A, 2, 3, 4 in two suits: Hearts and Spades.

The sample space must list all 8 individual cards, not just values or suits.

Option A is the only list that does this correctly.

16) Which statement best describes the probability of getting a Yellow and a number greater than 6?

Unlikely

Certain

Equally likely

Impossible

The die only has numbers 1–6, so it is impossible to roll a number greater than 6.

Even though Yellow is on the spinner, the number part makes the whole event impossible.

Explanation

The die only has numbers 1–6, so it is impossible to roll a number greater than 6.

Even though Yellow is on the spinner, the number part makes the whole event impossible.

17) What is the likelihood of landing on Blue and rolling an odd number?

3 out of 24

1 out of 24

6 out of 24

12 out of 24

To get this outcome, two things must happen:

Spin Blue (1 out of 4 chance)

Roll an odd number (1, 3, or 5 → 3 out of 6 chance)

The possible Blue-odd outcomes are:

(B,1), (B,3), (B,5) → 3 outcomes

There are 24 total outcomes, so probability = 3/24.

Explanation

To get this outcome, two things must happen:

Spin Blue (1 out of 4 chance)

Roll an odd number (1, 3, or 5 → 3 out of 6 chance)

The possible Blue-odd outcomes are:

(B,1), (B,3), (B,5) → 3 outcomes

There are 24 total outcomes, so probability = 3/24.

18) Which two outcomes are equally likely?

(R, 5) and (R, 6)

(B, 2) and (Y, 2)

(G, 3) and (Y, 1)

All pairs in A, B, and C are equally likely

The spinner is fair (all colors equal sized), and the die is fair (all numbers equal).

This means every color-number pair has the same probability.

So all pairs listed—(R,5), (R,6), (B,2), (Y,2), (G,3), (Y,1)—are equally likely.

Explanation

The spinner is fair (all colors equal sized), and the die is fair (all numbers equal).

This means every color-number pair has the same probability.

So all pairs listed—(R,5), (R,6), (B,2), (Y,2), (G,3), (Y,1)—are equally likely.

19) Which of the following outcomes is impossible for the experiment described?

(G, 4)

(Y, 6)

(Purple, 2)

(B, 1)

The spinner only has Red, Blue, Green, Yellow.

Purple never appears, so the pair (Purple, 2) cannot happen.

All the other pairs use colors that are actually on the spinner.

Explanation

The spinner only has Red, Blue, Green, Yellow.

Purple never appears, so the pair (Purple, 2) cannot happen.

All the other pairs use colors that are actually on the spinner.

20) How many outcomes are in the sample space for one spin and one roll?

4

24

6

12

Each spin (4 possibilities) can be combined with each roll (6 possibilities).

Multiplying them gives 24 total outcomes, representing all unique combinations of spinner + die.

Explanation

Each spin (4 possibilities) can be combined with each roll (6 possibilities).

Multiplying them gives 24 total outcomes, representing all unique combinations of spinner + die.

Identifying Outcomes in a Sample Space Quiz

1) A jar has letter tiles: A, A, B, C. One tile is drawn at random. Which sample space and counts are correct?

2) A game board spinner has 8 equal spaces numbered 1–8. Which is a correct description of an outcome and its likelihood?

3) You flip a fair coin twice. Which sample space lists all possible ordered outcomes?

4) A bag has 4 green, 4 yellow, and 4 purple beads. One bead is chosen at random. Which statement is true?

5) Which list shows all outcomes when choosing a day from a school week?

6) A number is chosen at random from the set {2, 4, 6, 8}. Which statement is true?

7) A spinner has 3 equal sections labeled Cat, Dog, Bird. Which outcome is impossible?

8) For two fair number cubes, which of the following is a correct set of possible sums?

9) You roll two fair number cubes. Which is the correct sample space size (number of outcomes)?

10) A spinner has 5 equal sections labeled 1, 2, 3, 4, 5. Which statement is true?

11) Which of the following lists represents the complete sample space for spinning the spinner once and rolling the number cube once (as ordered pairs Spinner, Die)?

12) Which list correctly shows all outcomes for rolling a fair number cube?

13) A fair coin is flipped and a fair 3-sided spinner labeled 1, 2, 3 is spun. Which statement is true?

14) A bag contains 3 red marbles and 2 blue marbles. One marble is drawn. Which outcome is impossible?

15) A standard deck is reduced to these 8 cards: A, 2, 3, 4 of Hearts and A, 2, 3, 4 of Spades. If one card is drawn at random, which is the correct sample space?

16) Which statement best describes the probability of getting a Yellow and a number greater than 6?

17) What is the likelihood of landing on Blue and rolling an odd number?

18) Which two outcomes are equally likely?

19) Which of the following outcomes is impossible for the experiment described?

20) How many outcomes are in the sample space for one spin and one roll?