Representing Sample Spaces For Compound Events Quiz

1) 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

2 (coin) × 6 (cube) = 12.

Explanation

2 (coin) × 6 (cube) = 12.

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

Bar graph

Pie chart

Line plot

Tree diagram

Tree diagrams list all outcomes step by step.

Explanation

Tree diagrams list all outcomes step by step.

3) 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 × 4 = 12.

Explanation

3 × 4 = 12.

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

H, T

HH, TT

HH, HT, TH

HH, HT, TH, TT

Two flips → HH, HT, TH, TT.

Explanation

Two flips → HH, HT, TH, TT.

5) 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

2 × 2 = 4.

Explanation

2 × 2 = 4.

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

9

12

18

24

3 × 6 = 18.

Explanation

3 × 6 = 18.

7) What is the probability of spinning “A” AND rolling a 4?

1/18

1/6

1/3

1/9

(1/3) × (1/6) = 1/18.

Explanation

(1/3) × (1/6) = 1/18.

8) How would you describe the likelihood of getting “B” and an even number?

Certain

Impossible

Very likely

Possible but not likely

(1/3) × (1/2) = 1/6 → small, so “possible but not likely.”

Explanation

(1/3) × (1/2) = 1/6 → small, so “possible but not likely.”

9) 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

One specific letter with one specific number = 1/18.

Explanation

One specific letter with one specific number = 1/18.

10) 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

Each coin branch splits into 4 die outcomes.

Explanation

Each coin branch splits into 4 die outcomes.

11) 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 × 4 = 16.

Explanation

4 × 4 = 16.

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

36

24

12

48

6 × 6 = 36.

Explanation

6 × 6 = 36.

13) 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 × 2 = 6.

Explanation

3 × 2 = 6.

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

6

5

8

9

3 × 2 = 6.

Explanation

3 × 2 = 6.

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

1/3

1/5

1/6

1/2

1 desired outcome out of 6 total → 1/6.

Explanation

1 desired outcome out of 6 total → 1/6.

16) How many branches extend from the “large” shirt option?

1

2

3

6

Large can be black or white → 2 branches.

Explanation

Large can be black or white → 2 branches.

17) 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

(1/2) × (1/4) = 1/8 → smallest among the choices.

Explanation

(1/2) × (1/4) = 1/8 → smallest among the choices.

18) 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 × ? = 15 → ? = 3.

Explanation

5 × ? = 15 → ? = 3.