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 = {2,4,6}; 3 is not even → no overlap.

Explanation

Even = {2,4,6}; 3 is not even → no overlap.

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

C = {5,6}; D = {5} → overlap at 5.

Explanation

C = {5,6}; D = {5} → overlap at 5.

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

Intersection = {3,5} → not mutually exclusive.

Explanation

Intersection = {3,5} → 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

{1,2} and {6} have no common outcome.

Explanation

{1,2} and {6} have no common outcome.

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 sets → not mutually exclusive.

Explanation

6 is in both sets → 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 can’t be two colors.

Explanation

One marble can’t be two colors.

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 red or blue → no overlap.

Explanation

Green is not red or blue → no overlap.

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.

Explanation

“Not blue” includes red and green.

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

That sequence is possible.

Explanation

That sequence is possible.

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

One card is a red circle → overlap exists.

Explanation

One card is a red circle → overlap exists.

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

A card can’t be two colors at once.

Explanation

A card can’t be two colors at once.

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

“Star” and “not star” can’t happen together.

Explanation

“Star” and “not star” can’t happen together.

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

One spin gives only one letter.

Explanation

One spin gives only one letter.

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 in both.

Explanation

Letters appearing twice: A, B, C. B is in both.

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; “appears once” is D or E.

Explanation

C appears twice; “appears once” is D or E.

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 that appear once are D and E; AD overlaps AE.

Explanation

Letters that appear once are D and E; AD overlaps AE.

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

The scenario allows students to be in both.

Explanation

The scenario allows students to be in both.

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 can’t be both at once.

Explanation

A day can’t be both at once.

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

One lunch can’t be vegan and chicken.

Explanation

One lunch can’t be vegan and chicken.

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

Multiple selections are allowed, so overlap is possible.

Explanation

Multiple selections are allowed, so overlap is possible.