Distinguishing Mutually Exclusive and Overlapping Events Quiz

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| Questions: 20 | Updated: Nov 10, 2025
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1) What is P(S)?

Explanation

120 ÷ 200 = 0.60

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About This Quiz
Distinguishing Mutually Exclusive And Overlapping Events Quiz - Quiz

This quiz focuses on differentiating between mutually exclusive events and overlapping events. You’ll learn how to apply the addition rule and interpret it correctly when events overlap. You’ll calculate probabilities for scenarios where events can happen together and when they can’t. By the end, you’ll have the tools to understand... see morewhen events are mutually exclusive or overlapping, along with how to compute their combined probabilities. see less

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2) What is P(M)?

Explanation

90 ÷ 200 = 0.45

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3) What is P(S and M)?

Explanation

50 ÷ 200 = 0.25

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4) What is P(S or M)?

Explanation

0.60 + 0.45 − 0.25 = 0.80

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5) Are S and M mutually exclusive?

Explanation

They overlap since 50 students are in both.

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

Explanation

200 − (120 + 90 − 50) = 40

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

Explanation

6 is in both sets.

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8) What is P(A or B)?

Explanation

(3/6) + (2/6) − (1/6) = 4/6

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

Explanation

One marble can’t be two colors.

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

Explanation

0.40 + 0.35 − 0.15 = 0.60

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

Explanation

They overlap because 15% take both.

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

Explanation

3 favorable out of 4 → 3/4.

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

Explanation

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

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

Explanation

13/52 + 4/52 − 1/52 = 16/52.

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

Explanation

The queen of hearts is in both events.

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

Explanation

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

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

Explanation

3 is common to both sets.

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18) What percent own a dog or a cat?

Explanation

55 + 30 − 20 = 65%.

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

Explanation

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

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

Explanation

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

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What is P(S)?
What is P(M)?
What is P(S and M)?
What is P(S or M)?
Are S and M mutually exclusive?
How many students are in neither Sports nor Music?
Let A = rolling an even number, and B = rolling a number greater than...
What is P(A or B)?
Let R = “red” and B = “blue.” Are R and B mutually exclusive?
In a class, 40% take Spanish (A), 35% take French (B), and 15% take...
For Q10, are A and B mutually exclusive?
Let A = “at least one head,” and B = “both heads.” What is P(A...
For Q12, why must subtraction be used in P(A or B)?
Event A: drawing a heart. Event B: drawing a queen. What is P(A or B)?
For Q14, are A and B mutually exclusive?
Let A = “odd,” and C = “a multiple of 3.” What is P(A or C)?
For Q16, are A and C mutually exclusive?
What percent own a dog or a cat?
Let B = “black” and N = “not black.” Are B and N mutually...
Let A = “drawing a face card,” and E = “drawing an even-numbered...
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