Finding Probabilities Of Mutually Exclusive Events Quiz

1) What is the probability of drawing a red or a blue marble?

20/30

8/30

12/30

10/30

Red = 12, Blue = 8 → Total = 12 + 8 = 20. Total marbles = 30 → Probability = 20/30.

Explanation

Red = 12, Blue = 8 → Total = 12 + 8 = 20. Total marbles = 30 → Probability = 20/30.

2) What is the probability of drawing a green or a yellow marble?

5/30

10/30

22/30

17/30

Green = 5, Yellow = 5 → Total = 10. Probability = 10/30.

Explanation

Green = 5, Yellow = 5 → Total = 10. Probability = 10/30.

3) What is the probability of drawing a red or a green marble?

5/30

12/30

17/30

7/30

Red = 12, Green = 5 → Total = 17. Probability = 17/30.

Explanation

Red = 12, Green = 5 → Total = 17. Probability = 17/30.

4) What is the probability of drawing a blue or a yellow marble?

8/30

5/30

25/30

13/30

Blue = 8, Yellow = 5 → Total = 13. Probability = 13/30.

Explanation

Blue = 8, Yellow = 5 → Total = 13. Probability = 13/30.

5) If event A is 'draw a red marble' and event B is 'draw a blue marble,' are A and B mutually exclusive?

Yes, because the jar is not evenly split

No, because some marbles are both red and blue

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

No, because the total is 30

Each marble has only one color, so both can’t occur together.

Explanation

Each marble has only one color, so both can’t occur together.

6) What is the probability of drawing a marble that is NOT red or blue?

12/30

20/30

10/30

30/30

Not red or blue = green + yellow = 5 + 5 = 10. Probability = 10/30.

Explanation

Not red or blue = green + yellow = 5 + 5 = 10. Probability = 10/30.

7) What is the probability of rolling a 1 or a 6?

1/6

2/6

3/6

4/6

Favorable outcomes: {1, 6} → 2 out of 6 total. Probability = 2/6.

Explanation

Favorable outcomes: {1, 6} → 2 out of 6 total. Probability = 2/6.

8) What is the probability of rolling an even number (2, 4, 6) or a 5?

3/6

2/6

5/6

4/6

Even numbers = {2, 4, 6}, plus 5 → total 4 favorable outcomes. Probability = 4/6.

Explanation

Even numbers = {2, 4, 6}, plus 5 → total 4 favorable outcomes. Probability = 4/6.

9) Let A = 'roll a number less than 3' and B = 'roll a number greater than 4.' Are A and B mutually exclusive?

Yes, because the outcomes do not overlap

No, because 3 is in both

No, because 4 is in both

Yes, because all numbers are even

A = {1, 2}, B = {5, 6} → no common numbers → mutually exclusive.

Explanation

A = {1, 2}, B = {5, 6} → no common numbers → mutually exclusive.

10) What is the probability of rolling a 2 or a 3 or a 6?

1/6

2/6

3/6

4/6

Favorable = {2, 3, 6} → 3 outcomes. Probability = 3/6.

Explanation

Favorable = {2, 3, 6} → 3 outcomes. Probability = 3/6.

11) What is the probability of landing on A or D?

2/8

4/8

5/8

3/8

A = 2 sections, D = 1 section → total 3. Probability = 3/8.

Explanation

A = 2 sections, D = 1 section → total 3. Probability = 3/8.

12) What is the probability of landing on B or C or E?

5/8

6/8

7/8

4/8

B = 2, C = 1, E = 2 → total 5. Probability = 5/8.

Explanation

B = 2, C = 1, E = 2 → total 5. Probability = 5/8.

13) Are the events 'landing on A' and 'landing on B' mutually exclusive on a single spin?

No, because some sections are both A and B

No, because there are two A’s

Yes, because one spin can land on only one section

Yes, because A and B have equal probability

A single spin lands on one section only → can’t land on both A and B.

Explanation

A single spin lands on one section only → can’t land on both A and B.

14) What is the probability of NOT landing on E or D?

3/8

4/8

5/8

6/8

E = 2, D = 1 → total 3. Not (E or D) = 8 − 3 = 5 → 5/8.

Explanation

E = 2, D = 1 → total 3. Not (E or D) = 8 − 3 = 5 → 5/8.

15) What is the probability of drawing a vowel or a consonant?

6/20

14/20

1

0

All tiles are vowels or consonants. Probability = (6 + 14) / 20 = 20/20 = 1.

Explanation

All tiles are vowels or consonants. Probability = (6 + 14) / 20 = 20/20 = 1.

16) What is the probability of drawing A or E?

2/20

3/20

6/20

5/20

A appears twice, E once → total 3. Probability = 3/20.

Explanation

A appears twice, E once → total 3. Probability = 3/20.

17) Let A = 'draw a vowel' and B = 'draw a consonant.' Are A and B mutually exclusive?

No, because a tile can be both

Yes, because there are 20 tiles

No, because there are more consonants

Yes, because a tile is either vowel or consonant, not both

A single tile can’t be both vowel and consonant.

Explanation

A single tile can’t be both vowel and consonant.

18) What is the probability the student prefers Soccer or Basketball?

12/30

9/30

28/30

21/30

Soccer = 12, Basketball = 9 → total 21. Probability = 21/30.

Explanation

Soccer = 12, Basketball = 9 → total 21. Probability = 21/30.

19) What is the probability the student prefers Baseball or Tennis?

7/30

9/30

19/30

30/30

Baseball = 7, Tennis = 2 → total 9. Probability = 9/30.

Explanation

Baseball = 7, Tennis = 2 → total 9. Probability = 9/30.

20) Are 'prefers Soccer' and 'prefers Basketball' mutually exclusive for one student?

Finding Probabilities of Mutually Exclusive Events Quiz