Distinguishing Mutually Exclusive And Overlapping Events Quiz

1) For Q10, are A and B mutually exclusive?

Yes, because P(A and B)<P(A or B)

No, because P(A and B)=0.15>0

Yes, because P(A)+P(B)=0.75

No, because languages are related

They overlap because 15% take both.

Explanation

They overlap because 15% take both.

2) Let A = “drawing a face card,” and E = “drawing an even-numbered red card.” Which statement is true?

A and E are mutually exclusive because face cards are not numbered

A and E overlap since queens are even

A and E overlap because jacks count as 11

A and E overlap because face cards can be even

Face cards have no numbers, so they can’t be even-numbered.

Explanation

Face cards have no numbers, so they can’t be even-numbered.

3) Let B = “black” and N = “not black.” Are B and N mutually exclusive?

No, because a pen can be both black and not black

Yes, because a pen cannot be both black and not black

No, because red and blue exist

No, because P(B)+P(N)=1

One pen can’t be both black and not black.

Explanation

One pen can’t be both black and not black.

4) What percent own a dog or a cat?

70%

75%

65%

85%

55 + 30 − 20 = 65%.

Explanation

55 + 30 − 20 = 65%.

5) For Q16, are A and C mutually exclusive?

Yes, because multiples of 3 are even

Yes, because odd and multiple of 3 never overlap

No, because 6 is a multiple of 3

No, because 3 is both odd and a multiple of 3

3 is common to both sets.

Explanation

3 is common to both sets.

6) Let A = “odd,” and C = “a multiple of 3.” What is P(A or C)?

1/2

2/3

3/4

5/6

Odd = {1,3,5}, multiples of 3 = {3,6}, total unique = 4 → 4/6 = 2/3.

Explanation

Odd = {1,3,5}, multiples of 3 = {3,6}, total unique = 4 → 4/6 = 2/3.

7) For Q14, are A and B mutually exclusive?

Yes, because suits and ranks differ

Yes, because a card can’t be both a heart and a queen

No, because the queen of hearts exists

No, because P(A)+P(B)>1

The queen of hearts is in both events.

Explanation

The queen of hearts is in both events.

8) Event A: drawing a heart. Event B: drawing a queen. What is P(A or B)?

13/52+4/52

14/52

(13/52)+(4/52)−(4/52)

(13/52)+(4/52)−(1/52)

13/52 + 4/52 − 1/52 = 16/52.

Explanation

13/52 + 4/52 − 1/52 = 16/52.

9) For Q12, why must subtraction be used in P(A or B)?

Because B is contained within A, so counting both adds overlap

Because A and B are mutually exclusive

Because probabilities must sum to 1

Because A and B have equal probability

B is part of A, so overlap must be subtracted.

Explanation

B is part of A, so overlap must be subtracted.

10) Let A = “at least one head,” and B = “both heads.” What is P(A or B)?

1/2

2/3

3/4

1

3 favorable out of 4 → 3/4.

Explanation

3 favorable out of 4 → 3/4.

11) What is P(S)?

0.50

0.45

0.75

0.60

120 ÷ 200 = 0.60

Explanation

120 ÷ 200 = 0.60

12) In a class, 40% take Spanish (A), 35% take French (B), and 15% take both. What is P(A or B)?

0.55

0.75

0.80

0.60

0.40 + 0.35 − 0.15 = 0.60

Explanation

0.40 + 0.35 − 0.15 = 0.60

13) Let R = “red” and B = “blue.” Are R and B mutually exclusive?

Yes, because a single draw cannot be both red and blue

No, because the jar has multiple colors

Yes, because P(R)+P(B)<1

No, because there are green marbles too

One marble can’t be two colors.

Explanation

One marble can’t be two colors.

14) What is P(A or B)?

2/6

3/6

4/6

5/6

(3/6) + (2/6) − (1/6) = 4/6

Explanation

(3/6) + (2/6) − (1/6) = 4/6

15) Let A = rolling an even number, and B = rolling a number greater than 4. Are A and B mutually exclusive?

Yes, because they cannot happen together

No, because 6 is both even and greater than 4

Yes, because P(A)+P(B)=1

No, because P(A and B)=0

6 is in both sets.

Explanation

6 is in both sets.

16) How many students are in neither Sports nor Music?

10

60

50

40

200 − (120 + 90 − 50) = 40

Explanation

200 − (120 + 90 − 50) = 40

17) Are S and M mutually exclusive?

No, because P(S and M)=0.25>0

Yes, because P(S)+P(M)>1

Yes, because P(S and M)=0

No, because P(S or M)=0.80

They overlap since 50 students are in both.

Explanation

They overlap since 50 students are in both.

18) What is P(S or M)?

0.85

0.70

0.80

0.60

0.60 + 0.45 − 0.25 = 0.80

Explanation

0.60 + 0.45 − 0.25 = 0.80

19) What is P(S and M)?

0.10

0.25

0.30

0.35

50 ÷ 200 = 0.25

Explanation

50 ÷ 200 = 0.25

20) What is P(M)?

0.25

0.50

0.60

0.45

90 ÷ 200 = 0.45

Explanation

90 ÷ 200 = 0.45

Distinguishing Mutually Exclusive and Overlapping Events Quiz

1) For Q10, are A and B mutually exclusive?

2)

What first name or nickname would you like us to use?

2) Let A = “drawing a face card,” and E = “drawing an even-numbered red card.” Which statement is true?

3) Let B = “black” and N = “not black.” Are B and N mutually exclusive?

4) What percent own a dog or a cat?

5) For Q16, are A and C mutually exclusive?

6) Let A = “odd,” and C = “a multiple of 3.” What is P(A or C)?

7) For Q14, are A and B mutually exclusive?

8) Event A: drawing a heart. Event B: drawing a queen. What is P(A or B)?

9) For Q12, why must subtraction be used in P(A or B)?

10) Let A = “at least one head,” and B = “both heads.” What is P(A or B)?

11) What is P(S)?

12) In a class, 40% take Spanish (A), 35% take French (B), and 15% take both. What is P(A or B)?

13) Let R = “red” and B = “blue.” Are R and B mutually exclusive?

14) What is P(A or B)?

15) Let A = rolling an even number, and B = rolling a number greater than 4. Are A and B mutually exclusive?

16) How many students are in neither Sports nor Music?

17) Are S and M mutually exclusive?

18) What is P(S or M)?

19) What is P(S and M)?

20) What is P(M)?