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 drawn in sequence from a standard deck without replacement. What is the probability that the first card is a king and the second card is a queen?

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

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

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

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

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

Question 3

If event A is 'driving over 85 miles per hour' and event B is 'getting in a car accident,' are these events independent or dependent?

Accepted Answer

Dependent, because speeding increases the chance of an accident.

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

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

Accepted Answer

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

Question 6

Which of the following scenarios describes dependent events?

Accepted Answer

Drawing two cards from a deck without replacement.

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 the correct formula for conditional probability?

Accepted Answer

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

Question 9

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 10

If $$P(A) = 0.3$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 11

A hospital reports that the probability of a successful ACL surgery is 0.95. What is the probability that three surgeries are all successful?

Accepted Answer

$$0.95^3$$

Question 12

A hospital reports that the probability of a successful ACL surgery is 0.95. What is the probability that none of three surgeries are successful?

Accepted Answer

$$0.05^3$$

Question 13

A hospital reports that the probability of a successful ACL surgery is 0.95. What is the probability that at least one of three surgeries is successful?

Accepted Answer

$$1 - 0.05^3$

Question 14

A medical student is matched to a residency position with probability 0.937, and 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 15

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

Accepted Answer

The events must occur at the same time.

Conditional Probability and the Multiplication Rule: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard