Understanding Mutually Exclusive Events Quiz

1) Event A: rolling an even number. Event B: rolling a 3. Are A and B mutually exclusive?

No, because 3 can occur with 2

Yes, because 3 is not on the die

No, because 3 is an even number

Yes, because no outcome is both even and 3

Even numbers are {2, 4, 6}.

3 is not even, so you can’t roll a number that is both even AND 3 at the same time.

No overlap → mutually exclusive.

Explanation

Even numbers are {2, 4, 6}.

3 is not even, so you can’t roll a number that is both even AND 3 at the same time.

No overlap → mutually exclusive.

2) Event C: rolling a number greater than 4. Event D: rolling a 5. Are C and D mutually exclusive?

No, because 5 is in both C and D

Yes, because C and D have no overlap

Yes, because 5 is not greater than 4

No, because they share outcomes 5 and 6

Event C = {5, 6} and Event D = {5}.

They share outcome 5, so they CAN happen together → not mutually exclusive.

Explanation

Event C = {5, 6} and Event D = {5}.

They share outcome 5, so they CAN happen together → not mutually exclusive.

3) Event E: rolling a prime number (2, 3, 5). Event F: rolling an odd number (1, 3, 5). Are E and F mutually exclusive?

Yes, because 2 is even

Yes, because primes are never odd

No, because outcomes 3 and 5 are in both events

No, because 1 is prime

Both lists include 3 and 5, so the events overlap.

If events share outcomes, they are NOT mutually exclusive.

Explanation

Both lists include 3 and 5, so the events overlap.

If events share outcomes, they are NOT mutually exclusive.

4) Event G: rolling a number less than 3 (1, 2). Event H: rolling a 6. Are G and H mutually exclusive?

No, because 1 and 6 overlap

Yes, because no outcome is both less than 3 and equal to 6

No, because 2 and 6 overlap

Yes, because both are less than 3

Numbers less than 3 are {1,2}.

6 is not one of them.

No overlap → mutually exclusive.

Explanation

Numbers less than 3 are {1,2}.

6 is not one of them.

No overlap → mutually exclusive.

5) If Event I: rolling an even number, and Event J: rolling a multiple of 3, are these events mutually exclusive?

Yes, because even numbers cannot be multiples of 3

No, because 2 is a multiple of 3

Yes, because 3 is odd

No, because 6 is both even and a multiple of 3

6 is in both groups:

Even numbers: {2, 4, 6}

Multiples of 3: {3, 6}

Since 6 overlaps, these events are NOT mutually exclusive.

Explanation

6 is in both groups:

Even numbers: {2, 4, 6}

Multiples of 3: {3, 6}

Since 6 overlaps, these events are NOT mutually exclusive.

6) Event K: drawing a red marble. Event L: drawing a blue marble. Are K and L mutually exclusive on a single draw?

No, because the bag has both colors

Yes, because there are more red than blue

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

No, because you draw without replacement

One marble cannot have two colors.

Red ≠ blue → cannot happen at same time → mutually exclusive.

Explanation

One marble cannot have two colors.

Red ≠ blue → cannot happen at same time → mutually exclusive.

7) Event M: drawing a green marble. Event N: drawing a primary color marble (red or blue). Are M and N mutually exclusive?

No, because green overlaps with red

Yes, because green is not red or blue

No, because green is a primary color

Yes, because the bag has no green

Green is NOT one of the primary colors in this bag.

A marble cannot be green and primary at the same time → mutually exclusive.

Explanation

Green is NOT one of the primary colors in this bag.

A marble cannot be green and primary at the same time → mutually exclusive.

8) Event P: drawing a marble that is not blue. Event Q: drawing a red marble. Are P and Q mutually exclusive?

No, because red marbles are included in not blue

Yes, because not blue excludes red

Yes, because red overlaps with blue

No, because blue includes red

“Not blue” includes red and green.

Red is part of Event P, so the events DO overlap → not mutually exclusive.

Explanation

“Not blue” includes red and green.

Red is part of Event P, so the events DO overlap → not mutually exclusive.

9) If two marbles were drawn one after another without replacement, are the events First marble is red and Second marble is blue mutually exclusive?

Yes, because you can’t draw two marbles

Yes, because colors can’t change

No, because red and blue are the same

No, because you can draw red first and blue second

You can absolutely draw a red marble first and then draw a blue one.

Since both can happen together → not mutually exclusive.

Explanation

You can absolutely draw a red marble first and then draw a blue one.

Since both can happen together → not mutually exclusive.

10) Event R: drawing a circle. Event S: drawing a red card. Are R and S mutually exclusive?

Yes, because circles can’t be red

Yes, because red cards are only triangles

No, because there is a red circle

No, because red squares are circles

Each shape includes one card of each color, so there is a red circle.

Shared outcome → not mutually exclusive.

Explanation

Each shape includes one card of each color, so there is a red circle.

Shared outcome → not mutually exclusive.

11) Event T: drawing a blue triangle. Event U: drawing a green shape. Are T and U mutually exclusive?

Yes, because a single card cannot be both blue and green

No, because some triangles are green and blue

No, because blue counts as green

Yes, because triangles cannot be blue

One card cannot be both blue AND green.

No overlap → mutually exclusive.

Explanation

One card cannot be both blue AND green.

No overlap → mutually exclusive.

12) Event V: drawing a star. Event W: drawing a shape that is not a star. Are V and W mutually exclusive?

No, because not star includes stars

Yes, because a card cannot be both star and not star

No, because star includes all shapes

Yes, because stars don’t exist in the deck

A card cannot be star AND not star.

That makes them mutually exclusive.

Explanation

A card cannot be star AND not star.

That makes them mutually exclusive.

13) Event X: landing on A. Event Y: landing on B. Are X and Y mutually exclusive in a single spin?

No, because A and B both appear

Yes, because A equals B

Yes, because one spin lands on only one letter

No, because you can land between letters

You only land on one section per spin.

The result can’t be A and B at the same time → mutually exclusive.

Explanation

You only land on one section per spin.

The result can’t be A and B at the same time → mutually exclusive.

14) Event Z: landing on a letter that appears twice. Event AA: landing on B. Are Z and AA mutually exclusive?

Yes, because B does not appear twice

Yes, because A appears twice, not B

No, because E appears once

No, because B appears twice and is in both events

Letters appearing twice: A, B, C.

B is included in both events → overlap → not mutually exclusive.

Explanation

Letters appearing twice: A, B, C.

B is included in both events → overlap → not mutually exclusive.

15) Event AB: landing on C. Event AC: landing on a letter that appears once. Are AB and AC mutually exclusive?

No, because C appears once

Yes, because C appears twice, not once

Yes, because C appears three times

No, because C and E both appear once

C appears twice, while AC contains letters appearing once (D and E).

No overlap → mutually exclusive.

Explanation

C appears twice, while AC contains letters appearing once (D and E).

No overlap → mutually exclusive.

16) Event AD: landing on D or E. Event AE: landing on a letter that appears exactly once. Are AD and AE mutually exclusive?

No, because D or E includes two letters that each appear once

Yes, because D and E appear twice

No, because A appears twice

Yes, because B appears twice

Letters appearing once: D and E.

Event AD also includes D and E, so they overlap → NOT mutually exclusive.

Explanation

Letters appearing once: D and E.

Event AD also includes D and E, so they overlap → NOT mutually exclusive.

17) Event AF: student is in band. Event AG: student is in choir. Are AF and AG mutually exclusive?

Yes, because you can’t be in both

Yes, because the school forbids overlap

No, because band equals choir

No, because some students can be in both band and choir

Some students participate in both, so the events overlap.

Therefore, not mutually exclusive.

Explanation

Some students participate in both, so the events overlap.

Therefore, not mutually exclusive.

18) Event AH: the day is a weekend. Event AI: the day is a weekday. Are AH and AI mutually exclusive?

No, because some days are both

Yes, because days are either weekend or weekday, not both

Yes, because weekends don’t exist

No, because weekdays include Saturday

A day cannot be both weekend and weekday.

No overlap → mutually exclusive.

Explanation

A day cannot be both weekend and weekday.

No overlap → mutually exclusive.

19) Event AJ: student chooses vegan. Event AK: student chooses chicken. Are AJ and AK mutually exclusive for one lunch choice?

No, because you can order two lunches

No, because vegan includes chicken

Yes, because a single lunch cannot be both vegan and chicken

Yes, because vegetarian equals vegan

A vegan meal cannot contain chicken.

No overlap → mutually exclusive.

Explanation

A vegan meal cannot contain chicken.

No overlap → mutually exclusive.

20) Event AL: respondent selects soccer. Event AM: respondent selects basketball. Are AL and AM mutually exclusive?

No, because respondents are allowed to select more than one sport

Yes, because you must pick exactly one

Yes, because soccer and basketball are the same

No, because baseball is an option

If students can choose more than one, soccer and basketball can be chosen together → not mutually exclusive.

Explanation

If students can choose more than one, soccer and basketball can be chosen together → not mutually exclusive.