Q: 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?

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

Q: What is the multiplication rule for the probability of two independent events $$A$$ and $$B$$?

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

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

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

Q: Which formula would you use to find the probability of both $$A$$ and $$B$$ occurring if $$A$$ and $$B$$ are dependent?

$$P(A \cap B) = P(A|B) \times P(B)$$

Q: If the probability of a surgery being successful is $$0.95$$, what is the probability that three surgeries are all successful (assuming independence)?

$$0.95 \times 0.95 \times 0.95$$

Question 1

Which of the following best describes independent events?

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

If you select a king from a deck of 52 cards, do not replace it, and then select a queen, are these events independent or dependent?

Accepted Answer

Dependent, because removing a card changes the probability for the second draw.

Question 4

What is the multiplication rule for the probability of two independent events $$A$$ and $$B$$?

Accepted Answer

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

Question 5

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

Accepted Answer

Dependent events

Question 6

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.2$$

Question 7

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

Accepted Answer

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

Question 8

Which formula would you use to find the probability of both $$A$$ and $$B$$ occurring if $$A$$ and $$B$$ are dependent?

Accepted Answer

$$P(A \cap B) = P(A|B) 	imes P(B)$$

Question 9

If the probability of a surgery being successful is $$0.95$$, what is the probability that three surgeries are all successful (assuming independence)?

Accepted Answer

$$0.95 	imes 0.95 	imes 0.95$$

Question 10

If the probability of a surgery being successful is $$0.95$$, what is the probability that none of three surgeries are successful?

Accepted Answer

$$0.05^3$$

Question 11

If the probability that a surgery is successful is $$0.95$$, what is the probability that at least one of three surgeries is successful?

Accepted Answer

$$1 - 0.05^3$

Question 12

A student is matched to a residency position with probability $$0.937. If $$the probability of getting one of their top three choices is $$0.56$$, what is the probability that a randomly selected student is matched and gets one of their top three choices?

Accepted Answer

$$0.937 	imes 0.56$$

Question 13

Which of the following is an example of independent events?

Accepted Answer

Tossing a coin and rolling a die

Question 14

If $$P(A|B) = P(A)$$, what does this imply about events $$A$$ and $$B$$?

Accepted Answer

They are independent.

Question 15

Which of the following is the correct formula for conditional probability?

Accepted Answer

$$P(A|B) = \frac{P(A \cap B)}{P(B)}$$

Conditional Probability and the Multiplication Rule: Independent and Dependent Events

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