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 die can show 1–6.

Explanation

A die can show 1–6.

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}

Two flips → HH, HT, TH, TT.

Explanation

Two flips → HH, HT, TH, TT.

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 outcomes are 2, 4, 6.

Explanation

Even outcomes are 2, 4, 6.

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

Possible colors: red, blue, green → 3.

Explanation

Possible colors: red, blue, green → 3.

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

One of 4 equal sections → 1/4.

Explanation

One of 4 equal sections → 1/4.

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 H: HH, HT, TH.

Explanation

At least one H: HH, HT, TH.

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

There are 13 hearts in a deck.

Explanation

There are 13 hearts in a deck.

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

12

36

24

6

6 × 6 = 36 ordered pairs.

Explanation

6 × 6 = 36 ordered pairs.

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

Favorable: {30, 40, 50} = 3 of 5 → 3/5.

Explanation

Favorable: {30, 40, 50} = 3 of 5 → 3/5.

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}

Primes 1–8 are 2, 3, 5, 7 (note: 1 is not prime).

Explanation

Primes 1–8 are 2, 3, 5, 7 (note: 1 is not prime).

11) What is the sample space for this survey?

{Dog, Cat, Bird, Fish}

{Dog, Cat}

{18, 12, 6, 4}

{40}

All pet types listed.

Explanation

All pet types listed.

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

1

4

2

30

Outcomes by category: Dog, Cat → 2.

Explanation

Outcomes by category: Dog, Cat → 2.

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)

6 out of 40 = 0.15 = 3/20.

Explanation

6 out of 40 = 0.15 = 3/20.

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 = 12+6+4 = 22 → 22/40 = 11/20.

Explanation

Not dog = 12+6+4 = 22 → 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 here are A and E.

Explanation

Vowels here are A and E.

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

3

8

6

9

2^3 = 8 outcomes.

Explanation

2^3 = 8 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

{1,2,3} → 3 of 5 → 3/5.

Explanation

{1,2,3} → 3 of 5 → 3/5.

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}

Multiples of 3 on a die: 3 and 6.

Explanation

Multiples of 3 on a die: 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 or yellow = 3+2 = 5 of 10 → 1/2.

Explanation

Blue or yellow = 3+2 = 5 of 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 × 2 = 6.

Explanation

3 × 2 = 6.

Understanding Sample Space and Probability Rules Quiz