$$\frac{1}{2} \times \frac{1}{6}$$

$$\frac{4}{52} \times \frac{4}{51}$$

$$P(A \text{ and } B) = P(A) \times P(B)$$

$$\frac{4}{52} \times \frac{3}{51}$$

$$P(A \text{ and } B) = P(A) \times P(B|A)$$

Question 1

Which of the following best describes independent events in probability?

Accepted Answer

Events where the occurrence of one does not affect the probability of the other.

Question 2

A coin is tossed and a die is rolled. What is the probability of getting a head on the coin and a 6 on the die?

Accepted Answer

$$\frac{1}{2} 	imes \frac{1}{6}$$

Question 3

Which of the following pairs of events are dependent?

Accepted Answer

Selecting a king from a deck, not replacing it, then selecting a queen.

Question 4

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.2$$

Question 5

Driving over 85 miles per hour and getting in a car accident are:

Accepted Answer

Dependent events

Question 6

Two cards are drawn from a deck without replacement. What is the probability that the first is a king and the second is a queen?

Accepted Answer

$$\frac{4}{52} 	imes \frac{4}{51}$$

Question 7

Which formula correctly expresses the multiplication rule for two independent events A and B?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 8

If $$P(A|B) = 0.3$$ and $$P(B) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.15$$

Question 9

Which scenario best illustrates the use of the multiplication rule for dependent events?

Accepted Answer

Drawing two cards from a deck without replacement.

Question 10

If $$P(A) = 0.7$$ and $$P(B|A) = 0.4$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.28$$

Question 11

Which of the following is NOT a requirement for two events to be independent?

Accepted Answer

The events must occur at the same time.

Question 12

A student draws two cards from a deck, one after the other, without replacement. What is the probability that both are aces?

Accepted Answer

$$\frac{4}{52} 	imes \frac{3}{51}$$

Question 13

Which of the following is an example of independent events?

Accepted Answer

Tossing a coin and rolling a die.

Question 14

If $$P(A) = 0.6$$, $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.3$$

Question 15

Which of the following best describes the multiplication rule for dependent events?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B|A)$$

Conditional Probability and the Multiplication Rule: Independent and Dependent Events

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