Q: Which formula correctly represents 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 selected in sequence from a standard deck without replacement. What is the probability of selecting a king and then a queen?

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

Q: Which of the following is true for the probability of two dependent events A and B?

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

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 and then rolling a 6?

Accepted Answer

$$\frac{1}{12}$$

Question 3

If event A is 'selecting a king from a deck of 52 cards' and event B is 'selecting a queen from the remaining deck without replacement,' are these events independent or dependent?

Accepted Answer

Dependent, because the outcome of A affects the probability of B.

Question 4

Which formula correctly represents 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 (A) and getting in a car accident (B) are:

Accepted Answer

Dependent events

Question 6

Two cards are selected in sequence from a standard deck without replacement. What is the probability of selecting a king and then a queen?

Accepted Answer

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

Question 7

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

Accepted Answer

$$0.2$$

Question 8

Which of the following is true for the probability of two dependent events A and B?

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

$$0.857$$

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 medical student is matched to a residency position is $$0.937$$, and the probability that the match is one of their top three choices given they are matched is $$0.756$$, what is the probability that a randomly selected student is matched to one of their top three choices?

Accepted Answer

$$0.708$$

Question 12

Which of the following is the correct way to calculate the probability that at least one of three independent surgeries is successful, given the probability of success for one surgery is $$p$$?

Accepted Answer

$$1 - (1-p)^3$

Question 13

A survey finds that 202 out of 225 adults who have ridden in a self-driving vehicle are aged 18-64. What is the probability that a randomly selected adult who has ridden in a self-driving vehicle is aged 18-64?

Accepted Answer

$$\frac{202}{225}$$

Question 14

Which of the following scenarios describes dependent events?

Accepted Answer

Selecting two cards from a deck without replacement.

Question 15

If $$P(A) = 0.3$$ and $$P(B) = 0.4$$ for independent events, what is $$P(A \cap B)$$?

Accepted Answer

$$0.12$$

Conditional Probability and the Multiplication Rule

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