Analyzing Compound Events In A Sample Space Quiz

1) A sample space contains all possible outcomes when rolling two dice. How many total outcomes are in this sample space?

36

24

12

48

6 × 6 = 36 possible ordered pairs.

Explanation

6 × 6 = 36 possible ordered pairs.

2) Event A is rolling an even number on a die, and Event B is rolling a number greater than 4. What outcomes are in the intersection of A and B?

{2, 4}

{6}

{5, 6}

{2, 4, 5, 6}

Even numbers {2,4,6}; greater than 4 is {5,6}; overlap = {6}.

Explanation

Even numbers {2,4,6}; greater than 4 is {5,6}; overlap = {6}.

3) In a deck of 52 cards, Event M is drawing a red card and Event N is drawing a face card. These events are:

Mutually exclusive

Complementary

Overlapping

Independent only

Some cards (red face cards) belong to both events, so they overlap.

Explanation

Some cards (red face cards) belong to both events, so they overlap.

4) A spinner has 8 equal sections numbered 1–8. Event X is landing on a prime number and Event Y is landing on an odd number. What is P(X∪Y)?

3/8

6/8

7/8

5/8

Primes {2,3,5,7}; odds {1,3,5,7}; union {1,2,3,5,7} → 5 of 8 = 5/8.

Explanation

Primes {2,3,5,7}; odds {1,3,5,7}; union {1,2,3,5,7} → 5 of 8 = 5/8.

5) When flipping a coin and rolling a die simultaneously, which represents the sample space correctly?

{(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}

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

{H1, H2, H3, T1, T2, T3}

12 separate outcomes listed individually

Each coin result pairs with all 6 die results (2×6=12).

Explanation

Each coin result pairs with all 6 die results (2×6=12).

6) Event A and Event B are mutually exclusive. If P(A)=0.3 and P(B)=0.25, what is P(A∪B)?

0.075

0.05

0.55

0.60

For mutually exclusive events, add probabilities → 0.3 + 0.25 = 0.55.

Explanation

For mutually exclusive events, add probabilities → 0.3 + 0.25 = 0.55.

7) A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. Event R is selecting a red marble and Event G is selecting a green marble. What type of events are R and G?

Overlapping

Mutually exclusive

Complementary

Dependent

You can’t draw both a red and green marble at the same time.

Explanation

You can’t draw both a red and green marble at the same time.

8) In a sample space of 50 outcomes, Event A contains 20 outcomes and Event B contains 15 outcomes. If A and B have 8 outcomes in common, how many outcomes are in A∪B?

35

23

43

27

n(A∪B) = 20 + 15 − 8 = 27.

Explanation

n(A∪B) = 20 + 15 − 8 = 27.

9) Two events are complementary if:

They have some outcomes in common

They cannot occur at the same time

Together they make up the entire sample space and have no overlap

They are independent

Complementary events cover all outcomes and don’t overlap.

Explanation

Complementary events cover all outcomes and don’t overlap.

10) A student randomly selects a day of the week. Event W is selecting a weekday and Event E is selecting a day that starts with the letter 'T'. What is P(W∩E)?

2/7

1/7

3/7

5/7

Weekdays {Mon–Fri}; starting with T {Tuesday, Thursday}; overlap = Tuesday → 1/7.

Explanation

Weekdays {Mon–Fri}; starting with T {Tuesday, Thursday}; overlap = Tuesday → 1/7.

11) How many students participate in sports only (not music)?

45

18

63

27

Sports only = 45 − 18 = 27.

Explanation

Sports only = 45 − 18 = 27.

12) What is the probability that a randomly selected student participates in either sports or music (or both)?

0.83

0.65

0.45

0.38

P(S∪M) = (45 + 38 − 18)/100 = 65/100 = 0.65.

Explanation

P(S∪M) = (45 + 38 − 18)/100 = 65/100 = 0.65.

13) How many students participate in neither sports nor music?

17

35

27

18

Neither = 100 − (45 + 38 − 18) = 35.

Explanation

Neither = 100 − (45 + 38 − 18) = 35.

14) What is the probability that a randomly selected student participates in music but NOT sports?

0.38

0.27

0.18

0.20

Music only = 38 − 18 = 20 → 20/100 = 0.20.

Explanation

Music only = 38 − 18 = 20 → 20/100 = 0.20.

15) Are the events 'participates in sports' and 'participates in music' mutually exclusive?

No, because 18 students participate in both

Yes, because some students do both

Yes, because they are different activities

Cannot be determined from the data

They overlap, so they are not mutually exclusive.

Explanation

They overlap, so they are not mutually exclusive.

16) A number is randomly selected from {1–10}. Event A is multiples of 3, Event B is factors of 12. How many outcomes are in A∩B?

1

2

3

4

Common outcomes are {3,6} → 2 outcomes.

Explanation

Common outcomes are {3,6} → 2 outcomes.

17) In a sample space, if Event A and Event B are mutually exclusive, which statement must be true?

P(A∪B)=P(A)×P(B)

P(A∩B)=0

P(A)+P(B)=1

A and B are complementary

Mutually exclusive → no overlap → intersection = 0.

Explanation

Mutually exclusive → no overlap → intersection = 0.

18) A card is drawn from a standard deck. Event K is drawing a King and Event H is drawing a Heart. What is P(K∪H)?

4/52

13/52

16/52

17/52

Kings (4) + Hearts (13) − King of Hearts (1) = 16/52.

Explanation

Kings (4) + Hearts (13) − King of Hearts (1) = 16/52.

19) Event A has 12 outcomes, Event B has 15 outcomes, and A∪B has 22 outcomes. How many outcomes are in A∩B?

5

3

7

10

Overlap = 12 + 15 − 22 = 5.

Explanation

Overlap = 12 + 15 − 22 = 5.

20) A spinner is divided into 12 equal sections: 4 red, 3 blue, 3 yellow, and 2 green. Event X is landing on a primary color (red, blue, yellow) and Event Y is landing on red or green. What is P(X∩Y)?

6/12

4/12

10/12

2/12

X∩Y means red only = 4 of 12 → 4/12.

Explanation

X∩Y means red only = 4 of 12 → 4/12.

Analyzing Compound Events in a Sample Space Quiz