Q: When rolling a six-sided die, what is the probability of rolling a number greater than 3 OR an even number? A) $$P(\u003e3) + P(\text{even}) B$$) $$P(\u003e3) + P(\text{even}) - P(\u003e3 \cap \text{even}) C$$) $$P(\u003e3) \times P(\text{even}) D$$) $$P(\u003e3) - P(\text{even})$$

B) $$P(\u003e3) + P(\text{even}) - P(\u003e3 \cap \text{even})$$

Q: Which of the following is NOT a correct application of the addition rule for probability? A) For mutually exclusive events: $$P(A \cup B) = P(A) + P(B) B) $$For non-mutually exclusive events: $$P(A \cup B) = P(A) + P(B) - P(A \cap B) C) $$For independent events: $$P(A \cup B) = P(A) \times P(B) D) $$For events with overlap: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

C) For independent events: $$P(A \cup B) = P(A) \times P(B)$$

Q: Suppose you roll a die. What is the probability of getting a number less than 3 or an odd number? A) $$P(\u003c3) + P(\text{odd}) - P(\u003c3 \cap \text{odd}) B$$) $$P(\u003c3) + P(\text{odd}) C$$) $$P(\u003c3) \times P(\text{odd}) D$$) $$P(\u003c3) - P(\text{odd})$$

A) $$P(\u003c3) + P(\text{odd}) - P(\u003c3 \cap \text{odd})$$

Question 1

Which of the following pairs of events are mutually exclusive?

A) Drawing a red card and drawing a king from a standard deck of cards.
B) Rolling a die and getting a 3 or getting an even number.
C) Getting heads when flipping a coin and getting tails.
D) Wearing a green shirt and wearing red shorts.

Accepted Answer

C) Getting heads when flipping a coin and getting tails.

Question 2

If events A and B are mutually exclusive, which formula correctly calculates the probability of A or B occurring?

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

Accepted Answer

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

Question 3

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a diamond or a king?

A) $$\frac{13}{52} + \frac{4}{52} - \frac{1}{52}
B$$) $$\frac{13}{52} + \frac{4}{52}
C$$) $$\frac{13}{52} 	imes \frac{4}{52}
D$$) $$\frac{13}{52} - \frac{4}{52}$$

Accepted Answer

A) $$\frac{13}{52} + \frac{4}{52} - \frac{1}{52}$$

Question 4

When rolling a six-sided die, what is the probability of rolling a number greater than 3 OR an even number?

A) $$P(\u003e3) + P(	ext{even})
B$$) $$P(\u003e3) + P(	ext{even}) - P(\u003e3 \cap 	ext{even})
C$$) $$P(\u003e3) 	imes P(	ext{even})
D$$) $$P(\u003e3) - P(	ext{even})$$

Accepted Answer

B) $$P(\u003e3) + P(	ext{even}) - P(\u003e3 \cap 	ext{even})$$

Question 5

A single card is randomly selected from a deck of cards. What is the probability of selecting an ace or a king?

A) $$\frac{4}{52} + \frac{4}{52}
B$$) $$\frac{8}{52}
C$$) $$\frac{4}{52} + \frac{4}{52} - 0
D$$) $$\frac{4}{52} 	imes \frac{4}{52}$$

Accepted Answer

C) $$\frac{4}{52} + \frac{4}{52} - 0$$

Question 6

Given two events, A and B, with $$P(A) = 0.5$$, $$P(B) = 0.3$$, and $$P(A \cap B) = 0.1$$, what is $$P(A \cup B)$$?

A) $$0.5 + 0.3
B$$) $$0.5 + 0.3 - 0.1
C$$) $$0.5 	imes 0.3
D$$) $$0.5 - 0.3 + 0.1$$

Accepted Answer

B) $$0.5 + 0.3 - 0.1$$

Question 7

In a group of 300 people, 112 are wearing red shorts, 88 are wearing green shirts, and 63 are wearing both. What is the probability that a randomly selected person is wearing red shorts or a green shirt?

A) $$\frac{112}{300} + \frac{88}{300}
B$$) $$\frac{112}{300} + \frac{88}{300} - \frac{63}{300}
C$$) $$\frac{112}{300} 	imes \frac{88}{300}
D$$) $$\frac{112}{300} - \frac{88}{300}$$

Accepted Answer

B) $$\frac{112}{300} + \frac{88}{300} - \frac{63}{300}$$

Question 8

Which statement best describes the difference between mutually exclusive and non-mutually exclusive events?

A) Mutually exclusive events can occur at the same time, non-mutually exclusive events cannot.
B) Mutually exclusive events cannot occur at the same time, non-mutually exclusive events can.
C) Both types of events can occur together.
D) Non-mutually exclusive events are always independent.

Accepted Answer

B) Mutually exclusive events cannot occur at the same time, non-mutually exclusive events can.

Question 9

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and A and B are mutually exclusive, what is $$P(A \cup B)$$?

A) $$0.4 + 0.5 - 0.2
B$$) $$0.4 + 0.5
C$$) $$0.4 	imes 0.5
D$$) $$0.4 - 0.5$$

Accepted Answer

B) $$0.4 + 0.5$$

Question 10

A die is rolled. What is the probability of getting a 3 or a 5?

A) $$\frac{1}{6} + \frac{1}{6}
B$$) $$\frac{2}{6}
C$$) $$\frac{1}{6} + \frac{1}{6} - 0
D$$) $$\frac{1}{6} 	imes \frac{1}{6}$$

Accepted Answer

C) $$\frac{1}{6} + \frac{1}{6} - 0$$

Question 11

Which of the following is NOT a correct application of the addition rule for probability?

A) For mutually exclusive events: $$P(A \cup B) = P(A) + P(B)
B) $$For non-mutually exclusive events: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)
C) $$For independent events: $$P(A \cup B) = P(A) 	imes P(B)
D) $$For events with overlap: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$

Accepted Answer

C) For independent events: $$P(A \cup B) = P(A) 	imes P(B)$$

Question 12

Suppose you roll a die. What is the probability of getting a number less than 3 or an odd number?

A) $$P(\u003c3) + P(	ext{odd}) - P(\u003c3 \cap 	ext{odd})
B$$) $$P(\u003c3) + P(	ext{odd})
C$$) $$P(\u003c3) 	imes P(	ext{odd})
D$$) $$P(\u003c3) - P(	ext{odd})$$

Accepted Answer

A) $$P(\u003c3) + P(	ext{odd}) - P(\u003c3 \cap 	ext{odd})$$

Question 13

If two events are NOT mutually exclusive, which term must be subtracted when calculating $$P(A \cup B)$$?

A) $$P(A)
B$$) $$P(B)
C$$) $$P(A \cap B)
D$$) $$P(A \cup B)$$

Accepted Answer

C) $$P(A \cap B)$$

Question 14

A card is drawn from a standard deck. What is the probability that the card is a heart or a queen?

A) $$\frac{13}{52} + \frac{4}{52} - \frac{1}{52}
B$$) $$\frac{13}{52} + \frac{4}{52}
C$$) $$\frac{13}{52} 	imes \frac{4}{52}
D$$) $$\frac{13}{52} - \frac{4}{52}$$

Accepted Answer

A) $$\frac{13}{52} + \frac{4}{52} - \frac{1}{52}$$

Question 15

Which scenario best illustrates non-mutually exclusive events?

A) Flipping a coin and getting heads or tails.
B) Drawing a card and getting a spade or a king.
C) Rolling a die and getting a 2 or a 5.
D) Selecting a person who is either a student or a teacher, but not both.

Accepted Answer

B) Drawing a card and getting a spade or a king.

Question 16

If $$P(A) = 0.2$$, $$P(B) = 0.4$$, and $$P(A \cap B) = 0.1$$, what is the probability that either A or B occurs?

A) $$0.2 + 0.4 - 0.1
B$$) $$0.2 + 0.4
C$$) $$0.2 	imes 0.4
D$$) $$0.2 - 0.4 + 0.1$$

Accepted Answer

A) $$0.2 + 0.4 - 0.1$$

Question 17

A person is randomly selected from a group. The probability they are wearing red shorts is $$0.37$$, and the probability they are wearing a green shirt is $$0.29. If 0.21 is $$the probability they are wearing both, what is the probability they are wearing red shorts or a green shirt?

A) $$0.37 + 0.29 - 0.21
B$$) $$0.37 + 0.29
C$$) $$0.37 	imes 0.29
D$$) $$0.37 - 0.29 + 0.21$$

Accepted Answer

A) $$0.37 + 0.29 - 0.21$$

Question 18

Which of the following is true for mutually exclusive events?

A) $$P(A \cap B) = 0
B$$) $$P(A \cap B) = P(A) 	imes P(B)
C$$) $$P(A \cap B) = P(A) + P(B)
D$$) $$P(A \cap B) = 1$$

Accepted Answer

A) $$P(A \cap B) = 0$$

Addition Rule in Probability: Mutually Exclusive and Non-Mutually Exclusive Events

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