Apply Mutually Exclusive Events Quiz (HSS.CP.B.7)

1) What is the probability that a randomly selected student plays a sport OR is in the drama club?

0.65

0.425

0.725

0.35

((85+60-15)/200=130/200=0.65).

Explanation

((85+60-15)/200=130/200=0.65).

2) Are the events “plays a sport” and “is in the drama club” mutually exclusive?

Yes, because some students do both activities

No, because 15 students participate in both activities

Yes, because the probabilities don’t add to 1

No, because 70 students do neither activity

(P(both)=15/200>0) → not mutually exclusive.

Explanation

(P(both)=15/200>0) → not mutually exclusive.

3) What is the probability that a randomly selected student plays a sport but is NOT in the drama club?

0.425

0.30

0.35

0.575

((85-15)/200=70/200=0.35).

Explanation

((85-15)/200=70/200=0.35).

4) If the events were mutually exclusive (no student did both), what would be the probability that a student plays a sport OR is in the drama club?

0.65

0.725

0.575

0.85

(85/200+60/200=145/200=0.725).

Explanation

(85/200+60/200=145/200=0.725).

5) A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a red marble OR a blue marble?

0.8

0.5

0.3

0.15

((5+3)/10=8/10=0.8).

Explanation

((5+3)/10=8/10=0.8).

6) Which of the following pairs of events are mutually exclusive when rolling a standard six-sided die?

Rolling a number greater than 4 and rolling a 6

Rolling an odd number and rolling a 3

Rolling a number less than 5 and rolling a 2

Rolling an even number and rolling a 5

A single roll can’t be even and 5 (5 is odd).

Explanation

A single roll can’t be even and 5 (5 is odd).

7) In a deck of 52 playing cards, what is the probability of drawing a heart OR a king?

13/52

17/52

16/52

4/52

(13/52+4/52-1/52=16/52) (subtract the king of hearts overlap).

Explanation

(13/52+4/52-1/52=16/52) (subtract the king of hearts overlap).

8) A spinner is divided into 8 equal sections: 3 red, 2 blue, 2 yellow, and 1 green. What is the probability of landing on red OR green?

3/8

1/2

5/8

1/4

((3+1)/8=4/8=1/2).

Explanation

((3+1)/8=4/8=1/2).

9) What is the probability that a randomly selected animal is a dog OR a cat?

0.75

0.45

0.30

0.675

((45+30)/100=75/100=0.75).

Explanation

((45+30)/100=75/100=0.75).

10) Are the events “the animal is a bird” and “the animal is a rabbit” mutually exclusive?

No, because both events can occur

Yes, because their probabilities are different

Yes, because an animal cannot be both a bird and a rabbit

No, because they are both treated at the clinic

One animal can’t be two species at once.

Explanation

One animal can’t be two species at once.

11) What is the probability that a randomly selected animal is NOT a dog?

0.45

0.75

0.88

0.55

(1-45/100=55/100=0.55).

Explanation

(1-45/100=55/100=0.55).

12) What is the probability that a randomly selected animal is a bird, rabbit, OR reptile?

0.12

0.25

0.20

0.08

((12+8+5)/100=25/100=0.25).

Explanation

((12+8+5)/100=25/100=0.25).

13) Two dice are rolled. Which pair of events is mutually exclusive?

The sum is 2 and the sum is 12

The sum is 7 and the sum is odd

The sum is greater than 8 and the sum is 10

Both dice show even numbers and the sum is 6

One outcome can’t have sum 2 and 12 at once.

Explanation

One outcome can’t have sum 2 and 12 at once.

14) At a school carnival, the probability of winning a stuffed animal is 0.15 and the probability of winning a goldfish is 0.20. If these events are mutually exclusive, what is the probability of winning a stuffed animal OR a goldfish?

0.03

0.15

0.35

0.05

(0.15+0.20=0.35).

Explanation

(0.15+0.20=0.35).

15) A weather forecast states there is a 30% chance of rain and a 25% chance of snow. If it cannot rain and snow at the same time, what is the probability of precipitation (rain OR snow)?

0.075

0.30

0.25

0.55

(0.30+0.25=0.55).

Explanation

(0.30+0.25=0.55).

16) What is the probability that a customer ordered coffee OR tea?

0.875

0.925

1.00

0.60

Only pastry (=15) → beverage total (=200-15=185). (185/200=0.925).

Explanation

Only pastry (=15) → beverage total (=200-15=185). (185/200=0.925).

17) Are the events “ordered coffee” and “ordered tea” mutually exclusive?

No, because some customers ordered both

Yes, because a customer orders either coffee or tea, not both

Yes, because they have different probabilities

Cannot be determined from the information given

Both (=120+80-185=15>0) → not mutually exclusive.

Explanation

Both (=120+80-185=15>0) → not mutually exclusive.

18) What is the probability that a customer ordered a pastry?

0.20

0.65

0.40

0.325

(40+25+15=80) pastry orders → (80/200=0.40).

Explanation

(40+25+15=80) pastry orders → (80/200=0.40).

19) In a class election, the probability that Maria wins is 0.35, the probability that James wins is 0.40, and the probability that Chen wins is 0.25. What is the probability that Maria OR James wins?

0.60

0.14

1.00

0.75

Only one winner → (0.35+0.40=0.75).

Explanation

Only one winner → (0.35+0.40=0.75).

20) A quality control inspector examines products and classifies them as “perfect,” “minor defect,” or “major defect.” If a product has a minor defect, can it also be classified as perfect?

No, these categories are mutually exclusive

Yes, if it meets certain criteria

Yes, depending on the inspector’s judgment

Cannot be determined without more information

One item can’t be in two exclusive categories.

Explanation

One item can’t be in two exclusive categories.