Sample Space & Probability Rules Quiz (HSS.CP.A.1)

1) A standard six-sided die is rolled once. What is the sample space for this experiment?

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

{1, 2, 3, 4, 5}

{2, 4, 6}

{1, 3, 5}

A standard die has six equally likely faces: 1, 2, 3, 4, 5, and 6. So the sample space must list all six.

Explanation

A standard die has six equally likely faces: 1, 2, 3, 4, 5, and 6. So the sample space must list all six.

2) A coin is flipped twice. Which of the following represents the complete sample space?

{HH, TT}

{H, T}

{HH, HT, TT}

{HH, HT, TH, TT}

Each flip can be H or T. Two flips produce 4 ordered outcomes: HH, HT, TH, TT. All must appear to be complete.

Explanation

Each flip can be H or T. Two flips produce 4 ordered outcomes: HH, HT, TH, TT. All must appear to be complete.

3) In the experiment of rolling a standard die, let Event A be 'rolling an even number.' Which subset represents Event A?

{1, 3, 5}

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

{2, 4, 6}

{2, 3, 4}

Even numbers on a die are 2, 4, and 6. These form the subset for the event.

Explanation

Even numbers on a die are 2, 4, and 6. These form the subset for the event.

4) A bag contains 3 red marbles, 2 blue marbles, and 1 green marble. If one marble is drawn at random, how many outcomes are in the sample space (by color)?

6

3

5

4

Color outcomes only depend on the available colors: red, blue, and green. That makes 3 distinct outcomes.

Explanation

Color outcomes only depend on the available colors: red, blue, and green. That makes 3 distinct outcomes.

5) A spinner is divided into 4 equal sections labeled A, B, C, and D. What is the probability of landing on section B?

1/4

1/2

1/3

3/8

With 4 equal sections, each section has a 1 out of 4 chance of being landed on.

Explanation

With 4 equal sections, each section has a 1 out of 4 chance of being landed on.

6) Two coins are flipped. Let Event E be 'getting at least one head.' Which outcomes are in Event E?

{TT}

{HH}

{HT, TH}

{HH, HT, TH}

“At least one head” includes HH, HT, and TH. Only TT has zero heads, so it’s excluded.

Explanation

“At least one head” includes HH, HT, and TH. Only TT has zero heads, so it’s excluded.

7) A card is drawn from a standard deck of 52 cards. Let Event F be 'drawing a heart.' How many outcomes are in Event F?

4

12

13

26

Each suit (hearts, diamonds, clubs, spades) has 13 cards, so Event F contains 13 outcomes.

Explanation

Each suit (hearts, diamonds, clubs, spades) has 13 cards, so Event F contains 13 outcomes.

8) In rolling two dice, how many total outcomes are in the sample space?

12

36

24

6

Each die has 6 outcomes.

6 × 6 = 36 ordered pairs in the sample space.

Explanation

Each die has 6 outcomes.

6 × 6 = 36 ordered pairs in the sample space.

9) A number is randomly selected from the set {10, 20, 30, 40, 50}. Let Event G be 'selecting a number greater than 25.' What is the probability of Event G?

3/5

2/5

1/5

4/5

Numbers greater than 25 are 30, 40, and 50 → 3 out of 5 numbers.

Explanation

Numbers greater than 25 are 30, 40, and 50 → 3 out of 5 numbers.

10) A spinner has 8 equal sections numbered 1 through 8. Let Event H be 'landing on a prime number.' Which subset represents Event H?

{1, 2, 3, 5, 7}

{2, 4, 6, 8}

{2, 3, 5, 7}

{1, 3, 5, 7}

Prime numbers between 1 and 8 are 2, 3, 5, and 7.

(1 is NOT prime.)

Explanation

Prime numbers between 1 and 8 are 2, 3, 5, and 7.

(1 is NOT prime.)

11) What is the sample space for this survey?

{Dog, Cat, Bird, Fish}

{Dog, Cat}

{18, 12, 6, 4}

{40}

The sample space lists all possible categories: Dog, Cat, Bird, Fish.

Explanation

The sample space lists all possible categories: Dog, Cat, Bird, Fish.

12) Let Event J be 'a student prefers a dog or a cat.' How many outcomes are in Event J?

1

4

2

30

Event J includes two categories: Dog and Cat → 2 outcomes.

Explanation

Event J includes two categories: Dog and Cat → 2 outcomes.

13) What is the probability that a randomly selected student from this survey prefers a bird?

6/40

0.15

3/20

All of the above (6/40 = 0.15 = 3/20)

Bird = 6 out of 40 →

6/40 = 3/20 = 0.15.

All three representations are the same probability.

Explanation

Bird = 6 out of 40 →

6/40 = 3/20 = 0.15.

All three representations are the same probability.

14) Let Event K be 'a student prefers a pet that is NOT a dog.' What is the probability of Event K?

18/40

11/20

9/20

21/40

Not dog = cat (12) + bird (6) + fish (4) = 22 students.

22/40 = 11/20.

Explanation

Not dog = cat (12) + bird (6) + fish (4) = 22 students.

22/40 = 11/20.

15) A jar contains tiles with the letters A, B, C, D, and E. One tile is drawn at random. Let Event M be 'drawing a vowel.' Which subset represents Event M?

{B, C, D}

{A, B, E}

{A}

{A, E}

Vowels in the set A–E are A and E, so they form the event subset.

Explanation

Vowels in the set A–E are A and E, so they form the event subset.

16) In the experiment of flipping three coins, how many outcomes are in the sample space?

3

8

6

9

Each flip has 2 outcomes →

2 × 2 × 2 = 8 total outcomes.

Explanation

Each flip has 2 outcomes →

2 × 2 × 2 = 8 total outcomes.

17) A box contains 5 cards numbered 1, 2, 3, 4, and 5. Let Event N be 'drawing a card with a number less than 4.' What is the probability of Event N?

1/5

2/5

4/5

3/5

Numbers less than 4: 1, 2, 3 → 3 out of 5 total options.

Explanation

Numbers less than 4: 1, 2, 3 → 3 out of 5 total options.

18) A standard die is rolled. Let Event P be 'rolling a number that is a multiple of 3.' Which outcomes are in Event P?

{3, 6, 9}

{1, 3, 6}

{3, 6}

{2, 3, 6}

The only multiples of 3 on a standard die are 3 and 6.

Explanation

The only multiples of 3 on a standard die are 3 and 6.

19) A spinner has 10 equal sections: 5 red, 3 blue, and 2 yellow. Let Event Q be 'landing on a blue or yellow section.' What is the probability of Event Q?

3/10

1/2

2/10

8/10

Blue = 3 sections

Yellow = 2 sections

3 + 2 = 5 favorable

Total = 10

5/10 = 1/2

Explanation

Blue = 3 sections

Yellow = 2 sections

3 + 2 = 5 favorable

Total = 10

5/10 = 1/2

20) In a class election, students can vote for President from 3 candidates and Vice President from 2 candidates. How many outcomes are in the sample space for voting for both positions?

6

5

3

2

3 choices for President

2 choices for Vice President

3 × 2 = 6 possible voting outcomes.

Explanation

3 choices for President

2 choices for Vice President

3 × 2 = 6 possible voting outcomes.

Understanding Sample Space and Probability Rules Quiz