Representing Sample Spaces For Compound Events Quiz

1) Two spinners each have 4 equal sections. The first has colors: red, blue, green, yellow. The second has shapes: circle, square, triangle, star. What is the total number of color–shape combinations?

8

16

12

20

4 colors × 4 shapes = 16 outcomes

Explanation

4 colors × 4 shapes = 16 outcomes

2) A sample space for choosing a pizza size (small, medium, large) and a topping (pepperoni, mushroom, sausage, olives) contains how many outcomes?

7

10

12

16

Sizes: 3

Toppings: 4

3 × 4 = 12 outcomes.

Explanation

Sizes: 3

Toppings: 4

3 × 4 = 12 outcomes.

3) Which compound event has a probability closest to 1?

Getting any outcome when spinning a spinner and rolling a die

Rolling a 7 on a standard number cube and flipping heads

Picking two specific cards from different decks

Flipping tails three times in a row

Getting any outcome when spinning a spinner + rolling a die is always 100% because something must happen.

The others are rare events.

Explanation

Getting any outcome when spinning a spinner + rolling a die is always 100% because something must happen.

The others are rare events.

4) An organized list shows 15 total outcomes for a compound event. If the first event has 5 possible outcomes, how many outcomes does the second event have?

2

3

5

10

5 × (second event outcomes) = 15

So second event = 15 ÷ 5 = 3.

Explanation

5 × (second event outcomes) = 15

So second event = 15 ÷ 5 = 3.

5) A compound event involves tossing a coin and picking a card from a deck of 4 cards (A, B, C, D). Which probability is closest to 0?

Getting heads or tails

Picking any card

Getting any outcome

Getting heads AND picking card A

Heads = 1/2

Card A = 1/4

Together = 1/8

This is the smallest probability—all others are large probabilities.

Explanation

Heads = 1/2

Card A = 1/4

Together = 1/8

This is the smallest probability—all others are large probabilities.

6) How many branches extend from the "large" shirt option?

1

2

3

6

Large splits into black and white → 2 branches.

Explanation

Large splits into black and white → 2 branches.

7) What is the probability of selecting a medium black shirt?

1/3

1/5

1/6

1/2

Only one outcome is “medium + black”

Out of 6 total outcomes → 1/6.

Explanation

Only one outcome is “medium + black”

Out of 6 total outcomes → 1/6.

8) How many total outcomes does this tree diagram represent (shirts and colors)?

6

5

8

9

Sizes: small, medium, large (3)

Colors: black, white (2)

3 × 2 = 6 total outcomes.

Explanation

Sizes: small, medium, large (3)

Colors: black, white (2)

3 × 2 = 6 total outcomes.

9) A student creates an organized list for choosing one fruit (apple, banana, orange) and one drink (milk, juice). How many outcomes should be in the complete list?

5

6

8

9

3 fruit options × 2 drink options = 6 total combinations.

Explanation

3 fruit options × 2 drink options = 6 total combinations.

10) In a sample space table for rolling two number cubes, how many cells (outcomes) would the table contain?

36

24

12

48

Each cube has 6 outcomes.

A sample space table would be 6 rows × 6 columns = 36 outcomes.

Explanation

Each cube has 6 outcomes.

A sample space table would be 6 rows × 6 columns = 36 outcomes.

11) A coin is flipped and a number cube (1–6) is rolled. How many total outcomes are in the sample space?

8

12

10

14

A coin has 2 outcomes (H, T).

A number cube has 6 outcomes (1–6).

To find total outcomes in the sample space, multiply:

2 × 6 = 8 total outcomes

Each coin outcome pairs with each number.

Explanation

A coin has 2 outcomes (H, T).

A number cube has 6 outcomes (1–6).

To find total outcomes in the sample space, multiply:

2 × 6 = 8 total outcomes

Each coin outcome pairs with each number.

12) A tree diagram is started for flipping a coin and rolling a 4-sided die. How many branches will extend from EACH coin outcome (H or T)?

2

3

4

8

From each coin outcome (H or T), the next step is rolling a die with 4 outcomes.

So each branch splits into 4 new branches.

Explanation

From each coin outcome (H or T), the next step is rolling a die with 4 outcomes.

So each branch splits into 4 new branches.

13) Which outcome has the same probability as getting "C" and rolling a 2?

Rolling any even number

Spinning any letter

Spinning “A” and rolling a 5

Getting any letter with any number

(C,2) is one specific pair.

(A,5) is also a single specific pair, so probability is 1/18—the same.

Outcomes involving groups (like “any even number”) have higher probability.

Explanation

(C,2) is one specific pair.

(A,5) is also a single specific pair, so probability is 1/18—the same.

Outcomes involving groups (like “any even number”) have higher probability.

14) How would you describe the likelihood of getting "B" and an even number?

Certain

Impossible

Very likely

Possible but not likely

Even numbers: 2, 4, 6 → 3 choices

Spinner B = 1 choice

So 1 × 3 = 3 favorable outcomes

Total = 18

Probability = 3/18 = 1/6

This is possible, but not very likely.

Explanation

Even numbers: 2, 4, 6 → 3 choices

Spinner B = 1 choice

So 1 × 3 = 3 favorable outcomes

Total = 18

Probability = 3/18 = 1/6

This is possible, but not very likely.

15) What is the probability of spinning "A" AND rolling a 4?

1/18

1/6

1/3

1/9

There is exactly one outcome that shows (A, 4).

Out of 18 total outcomes: 1/18.

Explanation

There is exactly one outcome that shows (A, 4).

Out of 18 total outcomes: 1/18.

16) If you spin the spinner once and roll the number cube once, how many total outcomes are possible?

9

12

18

24

Spinner: 3 outcomes

Cube: 6 outcomes

3 × 6 = 18

Explanation

Spinner: 3 outcomes

Cube: 6 outcomes

3 × 6 = 18

17) A bag contains a red marble and a blue marble. Another bag contains a green marble and a yellow marble. If you pick one marble from each bag, how many outcomes are in the sample space?

4

3

2

6

Bag 1: red, blue

Bag 2: green, yellow

Possible pairs: (red,green), (red,yellow), (blue,green), (blue,yellow) → 4 outcomes

Explanation

Bag 1: red, blue

Bag 2: green, yellow

Possible pairs: (red,green), (red,yellow), (blue,green), (blue,yellow) → 4 outcomes

18) When flipping a coin twice, which organized list shows ALL possible outcomes?

H, T

HH, TT

HH, HT, TH

HH, HT, TH, TT

Each flip has 2 outcomes.

Two flips → 4 combinations:

first H then H

first H then T

first T then H

first T then T

All must be included, so D is correct.

Explanation

Each flip has 2 outcomes.

Two flips → 4 combinations:

first H then H

first H then T

first T then H

first T then T

All must be included, so D is correct.

19) A restaurant offers 3 types of bread (white, wheat, rye) and 4 types of meat (turkey, ham, roast beef, chicken). How many different sandwich combinations are possible?

7

10

12

16

3 bread choices × 4 meat choices = 12 outcomes?

Wait—let’s check:

WHITE → turkey, ham, roast beef, chicken

WHEAT → turkey, ham, roast beef, chicken

RYE → turkey, ham, roast beef, chicken

That’s 3 × 4 = 12.

Correct answer is C (12), not 16.

(Option D is incorrect because 4 meats × 4 breads ≠ 16.)

Explanation

3 bread choices × 4 meat choices = 12 outcomes?

Wait—let’s check:

WHITE → turkey, ham, roast beef, chicken

WHEAT → turkey, ham, roast beef, chicken

RYE → turkey, ham, roast beef, chicken

That’s 3 × 4 = 12.

Correct answer is C (12), not 16.

(Option D is incorrect because 4 meats × 4 breads ≠ 16.)

20) Which method would be MOST useful for showing all possible outcomes when spinning two different spinners?

Bar graph

Pie chart

Line plot

Tree diagram

A tree diagram shows each possible path from the first event to the second.

It organizes outcomes clearly, especially when each event has multiple options.

Bar graphs, pie charts, and line plots do NOT show combinations.

Explanation

A tree diagram shows each possible path from the first event to the second.

It organizes outcomes clearly, especially when each event has multiple options.

Bar graphs, pie charts, and line plots do NOT show combinations.

Representing Sample Spaces for Compound Events Quiz

1) Two spinners each have 4 equal sections. The first has colors: red, blue, green, yellow. The second has shapes: circle, square, triangle, star. What is the total number of color–shape combinations?

2) A sample space for choosing a pizza size (small, medium, large) and a topping (pepperoni, mushroom, sausage, olives) contains how many outcomes?

3) Which compound event has a probability closest to 1?

4) An organized list shows 15 total outcomes for a compound event. If the first event has 5 possible outcomes, how many outcomes does the second event have?

5) A compound event involves tossing a coin and picking a card from a deck of 4 cards (A, B, C, D). Which probability is closest to 0?

6) How many branches extend from the "large" shirt option?

7) What is the probability of selecting a medium black shirt?

8) How many total outcomes does this tree diagram represent (shirts and colors)?

9) A student creates an organized list for choosing one fruit (apple, banana, orange) and one drink (milk, juice). How many outcomes should be in the complete list?

10) In a sample space table for rolling two number cubes, how many cells (outcomes) would the table contain?

11) A coin is flipped and a number cube (1–6) is rolled. How many total outcomes are in the sample space?

12) A tree diagram is started for flipping a coin and rolling a 4-sided die. How many branches will extend from EACH coin outcome (H or T)?

13) Which outcome has the same probability as getting "C" and rolling a 2?

14) How would you describe the likelihood of getting "B" and an even number?

15) What is the probability of spinning "A" AND rolling a 4?

16) If you spin the spinner once and roll the number cube once, how many total outcomes are possible?

17) A bag contains a red marble and a blue marble. Another bag contains a green marble and a yellow marble. If you pick one marble from each bag, how many outcomes are in the sample space?

18) When flipping a coin twice, which organized list shows ALL possible outcomes?

19) A restaurant offers 3 types of bread (white, wheat, rye) and 4 types of meat (turkey, ham, roast beef, chicken). How many different sandwich combinations are possible?

20) Which method would be MOST useful for showing all possible outcomes when spinning two different spinners?