Q: Suppose two cards are drawn in sequence from a standard deck of 52 cards 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 coin is tossed and a die is rolled. What is the probability of tossing a head and then rolling a 6?

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

Q: If 73.6% of matched medical students got one of their top three choices, and 18,465 students were matched, what is the probability that a randomly selected senior was matched with a residency position and it was one of their top three choices?

$$\frac{18,465}{19,755} \times 0.736$$

Question 1

Suppose two cards are drawn in sequence from a standard deck of 52 cards 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 2

A survey of 10,330 U.S. adults found that 3,280 are interested in orbiting Earth in a private spacecraft, and 421 of these are aged 18 to 29. What is the probability that a randomly selected adult is 18 to 29 years old, given that they are interested in orbiting Earth in a private spacecraft?

Accepted Answer

$$\frac{421}{3280}$$

Question 3

Which of the following pairs of events are independent?

Accepted Answer

Tossing a coin and getting a head, and rolling a die and getting a 6

Question 4

If the probability that an ACL surgery is successful is 0.95, what is the probability that all three surgeries are successful (assuming independence)?

Accepted Answer

$$0.95^3$$

Question 5

A coin is tossed and a die is rolled. What is the probability of tossing a head and then rolling a 6?

Accepted Answer

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

Question 6

Which of the following best describes dependent events?

Accepted Answer

The occurrence of one event affects the probability of the other event.

Question 7

For ACL surgery, the probability of success is 0.95. What is the probability that none of three surgeries are successful?

Accepted Answer

$$(1 - 0.95)^3$

Question 8

If 73.6% of matched medical students got one of their top three choices, and 18,465 students were matched, what is the probability that a randomly selected senior was matched with a residency position and it was one of their top three choices?

Accepted Answer

$$\frac{18,465}{19,755} 	imes 0.736$$

Question 9

Which formula represents the conditional probability of event B given event A?

Accepted Answer

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

Question 10

Which of the following scenarios best illustrates the use of the multiplication rule for independent events?

Accepted Answer

Finding the probability of flipping a head and rolling a 4 on a die

Question 11

A medical student is matched with a residency position. If the probability of being matched with one of their top three choices is 0.736, what is the probability that a matched student did NOT get one of their top three choices?

Accepted Answer

$$1 - 0.736$$

Question 12

Which of the following is NOT a characteristic of independent events?

Accepted Answer

The occurrence of one event changes the probability of the other.

Question 13

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

Accepted Answer

$$0.4 	imes 0.5$$

Question 14

Which of the following real-life situations involves dependent events?

Accepted Answer

Drawing two cards from a deck without replacement

Question 15

If the probability of an event is 0.2, what is the probability that the event does NOT occur in three independent trials?

Accepted Answer

$$(1 - 0.2)^3$

Conditional Probability and the Multiplication Rule – Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard