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

We want the probability of selecting red OR blue.

Since a marble cannot be both red and blue, these events are mutually exclusive, so we can ADD their counts:

Red marbles = 12

Blue marbles = 8

Total favorable outcomes = 12 + 8 = 20

Total marbles = 30

So the probability is 20/30.

Explanation

We want the probability of selecting red OR blue.

Since a marble cannot be both red and blue, these events are mutually exclusive, so we can ADD their counts:

Red marbles = 12

Blue marbles = 8

Total favorable outcomes = 12 + 8 = 20

Total marbles = 30

So the probability is 20/30.

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

5/30

10/30

22/30

17/30

Green and yellow are separate colors, so the events do not overlap.

Add the totals:

Green = 5

Yellow = 5

Total = 10 favorable marbles

Probability = 10/30.

Explanation

Green and yellow are separate colors, so the events do not overlap.

Add the totals:

Green = 5

Yellow = 5

Total = 10 favorable marbles

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 and green are also mutually exclusive colors.

Red = 12

Green = 5

Total = 17

Probability = 17/30.

Explanation

Red and green are also mutually exclusive colors.

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

Add the two mutually exclusive outcomes:

Blue = 8

Yellow = 5

Total = 13 marbles

Probability = 13/30.

Explanation

Add the two mutually exclusive outcomes:

Blue = 8

Yellow = 5

Total = 13 marbles

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

A marble has exactly one color.

Since no marble can be red and blue at the same time, the events cannot happen together, which means they are mutually exclusive.

Explanation

A marble has exactly one color.

Since no marble can be red and blue at the same time, the events cannot happen together, which means they are mutually exclusive.

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.

Green = 5

Yellow = 5

Total = 10

Probability = 10/30.

Explanation

Not red or blue = green + yellow.

Green = 5

Yellow = 5

Total = 10

Probability = 10/30.

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

1/6

2/6

3/6

4/6

The outcomes {1, 6} are mutually exclusive, so add them.

There are 2 favorable outcomes out of 6 possible rolls → 2/6.

Explanation

The outcomes {1, 6} are mutually exclusive, so add them.

There are 2 favorable outcomes out of 6 possible rolls → 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 → 3 outcomes

Add 5 → 1 more outcome

Total favorable = 4 outcomes

Probability = 4/6.

Explanation

Even numbers: 2, 4, 6 → 3 outcomes

Add 5 → 1 more outcome

Total favorable = 4 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}

There are no shared outcomes, so the two events cannot happen together, meaning they are mutually exclusive.

Explanation

A = {1, 2}

B = {5, 6}

There are no shared outcomes, so the two events cannot happen together, meaning they are 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 outcomes: {2, 3, 6} → 3 outcomes

Probability = 3/6

Explanation

Favorable outcomes: {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 appears twice.

D appears once.

Total favorable = 2 + 1 = 3

Probability = 3/8

Explanation

A appears twice.

D appears once.

Total favorable = 2 + 1 = 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 sections

C → 1 section

E → 2 sections

Total = 5 favorable

Probability = 5/8.

Explanation

B → 2 sections

C → 1 section

E → 2 sections

Total = 5 favorable

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 stops on one section only.

It cannot land on both A and B at the same time → mutually exclusive.

Explanation

A single spin stops on one section only.

It cannot land on both A and B at the same time → mutually exclusive.

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

3/8

4/8

5/8

6/8

E = 2 sections

D = 1 section

Total excluded = 3

Remaining = 8 – 3 = 5

Probability = 5/8.

Explanation

E = 2 sections

D = 1 section

Total excluded = 3

Remaining = 8 – 3 = 5

Probability = 5/8.

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

6/20

14/20

1

0

Every tile must be either vowel OR consonant.

There are no other possibilities → probability = 1 (100%).

Explanation

Every tile must be either vowel OR consonant.

There are no other possibilities → probability = 1 (100%).

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

2/20

3/20

6/20

5/20

A appears twice,

E appears once → total = 3 favorable tiles

Probability = 3/20.

Explanation

A appears twice,

E appears once → total = 3 favorable tiles

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 tile cannot belong to both groups simultaneously.

Vowels and consonants are distinct categories → mutually exclusive.

Explanation

A tile cannot belong to both groups simultaneously.

Vowels and consonants are distinct categories → mutually exclusive.

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

12/30

9/30

28/30

21/30

Soccer = 12

Basketball = 9

Total = 12 + 9 = 21

Since students pick only one favorite, events are mutually exclusive → probabilities add.

Explanation

Soccer = 12

Basketball = 9

Total = 12 + 9 = 21

Since students pick only one favorite, events are mutually exclusive → probabilities add.

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?

No, because some students like both

Yes, because Soccer is more popular

No, because the total is 30

Yes, because each student reports only one favorite

Students choose one favorite sport on the survey.

A student cannot choose soccer AND basketball simultaneously → events are mutually exclusive.

Explanation

Students choose one favorite sport on the survey.

A student cannot choose soccer AND basketball simultaneously → events are mutually exclusive.

Finding Probabilities of Mutually Exclusive Events Quiz

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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