Free Printable Mutually Exclusive Events

1.

Which of the following best describes mutually exclusive events?

a)

Events that can occur at the same time.

b)

Events that cannot occur at the same time.

c)

Events that are independent of each other.

d)

Events that have the same probability.

e)

None of these.

2.

If $P(A) = 0.3$ and $P(B) = 0.4$ , and events A and B are mutually exclusive, what is $P(A \cup B)$ ?

a)

$0.12$

b)

$0.7$

c)

$0.1$

d)

$0.3$

e)

$0.4$

3.

What is the probability of the complement of an event A, if $P(A) = 0.65$ ?

a)

$0.35$

b)

$0.65$

c)

$0.45$

d)

$0.25$

e)

$1$

4.

Which of the following is the Addition Rule for probabilities of two events A and B?

a)

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

b)

$P(A \cup B) = P(A) \cdot P(B)$

c)

$P(A \cup B) = P(A) + P(B)$

d)

$P(A \cup B) = P(A) - P(B)$

e)

$P(A\cap B)=P(A)+P(B)$

5.

If two events A and B are mutually exclusive, what is $P(A \cap B)$ ?

a)

$0$

b)

$1$

c)

$P(A) \cdot P(B)$

d)

$P(A) + P(B)$

e)

$P(A)-P(B)$

6.

In a deck of 52 cards, what is the probability of drawing either a heart or a club?

a)

$\frac{1}{2}$

b)

$\frac{1}{4}$

c)

$\frac{1}{3}$

d)

$\frac{3}{4}$

e)

$1$

7.

Which of the following statements is true about complementary events?

a)

They are always mutually exclusive.

b)

They can occur at the same time.

c)

Their probabilities add up to 1.

d)

They are independent.

e)

None of these.

8.

What equation do you use when the events are not mutually exclusive?

a)

P (A or B) = P (AB) - P (A+B)

b)

P (A or B) = P (A) + P (B)

c)

P (A or B) = P (A) + P (B) - P (A and B)

d)

P (A or B) = P (A) - P (B)

e)

P (A and B) = P (A) + P (B)

9.

If you draw one card from a standard deck, what is the probability of drawing a spade or a red card?

a)

1/4

b)

1/2

c)

3/4

d)

Not possible

e)

3/5

10.

If you roll one die, what is the probability of getting an even number or a multiple of 3?

a)

1/3

b)

2/3

c)

1/2

d)

1/6

e)

1/4

11.

A high school math teacher has 78 students. Of those students, 35 participate in the musical and 32 are on a sports team. There are 16 students who are not in the musical or on a sports team. One student from the 78 students will be selected at random. Let event M represent the event of selecting a student in the musical, and let event S represent the event of selecting a student on a sports team.

Are M and S mutually exclusive events?

a)

No, because $P\left(M\cap S\right)=\frac{5}{78}$

b)

No, because $P\left(M\cap S\right)=\frac{48}{78}$

c)

No, because $P\left(M\cap S\right)=\frac{62}{78}$

d)

Yes, because $P\left(M\cap S\right)=\frac{5}{78}$

e)

Yes, because $P\left(M\cap S\right)=\frac{62}{78}$

12.

As a promotion, the first 50 customers who entered a certain store at a mall were asked to choose from one of two discounts. The first discount choice was 20% off all purchases made that day. The second discount choice was 10% off all purchases for the week. Of those who received the discounts, 28 chose the first discount and 22 chose the second discount. One customer will be selected at random from those who received a discount. Let F represent the event that the selected person chose the first discount, and let S represent the event that the selected person chose the second discount.

Are F and S mutually exclusive events?

a)

Yes, because $P\left(F\cap S\right)=0$

b)

Yes, because $P\left(F\cap S\right)=0.12$

c)

Yes, because $P\left(F\cap S\right)=1$

d)

No, because $P\left(F\cap S\right)=0$

e)

No, because $P\left(F\cap S\right)=1$

13.

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1.

a)

Events A and B are independent.

b)

Events A and B are mutually exclusive.

c)

Either A or B always occurs.

d)

Events A and B are complementary.

e)

None of these statements are correct.

14.

At a local high school, 60% of students have access to a laptop, 30% have access to a tablet, and 20% have access to both. The proportion of students that have access to neither a laptop or a tablet is:

a)

0%

b)

10%

c)

30%

d)

80%

e)

90%

15.

If P(A) = 0.7, P(~B) = 0.4, and P(A and B) = 0.5, find P(A or B):

a)

1.3

b)

0.6

c)

0.8

d)

0.1

e)

1

16.

At a local high school, there are 100 students enrolled in various AP courses. There are 31 students enrolled in AP Statistics, 52 students enrolled in AP Chemistry, and 15 students enrolled in AP Latin. Ten students study both AP Statistics and AP Chemistry, five students study both AP Statistics and AP Latin, eight students study both AP Chemistry and AP Latin, and three students study all three of these AP subjects. What is the probability that a student takes an AP course other than these three?

a)

9%

b)

12%

c)

22%

d)

78%

e)

93%

17.

An experiment has three mutually exclusive outcomes, A, B, and C. If P(A) = 0.18, P(B) = 0.56, and P(C) = 0.26, which of the following must be true?

I. A and C are independent.

II. P(A and B) = 0

III. P(B or C) = P(B) + P(C)

a)

I only

b)

I and II only

c)

I and III only

d)

II and III only

e)

I, II, and III

18.

Which of the following statements is true for two events, each with probability greater than zero?

a)

If the events are mutually exclusive, they must be independent.

b)

If the events are independent, they must be mutually exclusive.

c)

If the events are not mutually exclusive, they must be independent.

d)

If the events are not independent, they must be mutually exclusive.

e)

If the events are mutually exclusive, they cannot be independent.

19.

The enrollment at a local high school is 1400 students. Suppose 550 students take French, 700 take Algebra, and 400 take both French and Algebra. What is the probability that a student selected randomly takes French or Algebra?

a)

1250/1400

b)

700/1400

c)

550/1400

d)

850/1400

e)

1400/1400

20.

Which of the following shows how to determine P(skateboard or rollerblades)?

a)

48/100 + 42/100 - 39/100

b)

39/100 + 3/100 - 49/100

c)

49/100 + 9/100 - 3/100

d)

9/100 + 3/100 - 39/100

e)

none of these are correct

Mutually Exclusive Events

Total questions: 20

Worksheet time: 10mins

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