Q: If 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 coin is tossed and a die is rolled. What is the probability of getting a head and a 6?

$$ \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} $$

Q: Of the matched seniors, 75.6% got one of their top three choices. What is the probability that a randomly selected senior was matched and got one of their top three choices?

$$ \frac{18,108}{19,326} \times 0.756 $$

Q: If $$P(A) = 0.7$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.35$$, are events A and B independent?

Yes, because $$0.7 \times 0.5 = 0.35.$$

Q: A bag contains 5 red balls and 7 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

$$ \frac{5}{12} \times \frac{4}{11} $$

Question 1

Which of the following best describes conditional probability?

Accepted Answer

The probability of an event occurring, given that another event has already occurred.

Question 2

If 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 3

A survey found that 225 adults have ridden as a passenger in a self-driving vehicle, and 202 of them are 18 to 64 years old. What is the probability that a randomly selected adult who has ridden as a passenger is 18 to 64 years old?

Accepted Answer

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

Question 4

Which of the following pairs of events are independent?

Accepted Answer

Tossing a coin and rolling a die.

Question 5

If the probability of an event A is $$0.4$$ and the probability of event B is $$0.5$$, and A and B are independent, what is the probability that both A and B occur?

Accepted Answer

$$ 0.4 	imes 0.5 = 0.2 $$

Question 6

A manufacturer claims that 3% of all tires produced are defective. If you buy a set of four tires, what is the probability that none are defective?

Accepted Answer

$$ (0.97)^4$ $$

Question 7

Using the same tire scenario, what is the probability that at least one tire is defective?

Accepted Answer

$$ 1 - (0.97)^4$ $$

Question 8

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

Accepted Answer

$$ \frac{1}{2} 	imes \frac{1}{6} = \frac{1}{12} $$

Question 9

In a recent year, 18,108 out of 19,326 U.S. MD seniors were matched with residency positions. What is the probability that a randomly selected senior was matched?

Accepted Answer

$$ \frac{18,108}{19,326} $$

Question 10

Of the matched seniors, 75.6% got one of their top three choices. What is the probability that a randomly selected senior was matched and got one of their top three choices?

Accepted Answer

$$ \frac{18,108}{19,326} 	imes 0.756 $$

Question 11

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 12

If two events are dependent, which of the following is true?

Accepted Answer

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

Question 13

Which of the following is an example of dependent events?

Accepted Answer

Drawing two cards from a deck without replacement.

Question 14

If $$P(A) = 0.7$$, $$P(B) = 0.5$$, and $$P(A \cap B) = 0.35$$, are events A and B independent?

Accepted Answer

Yes, because $$0.7 	imes 0.5 = 0.35.$$

Question 15

A bag contains 5 red balls and 7 blue balls. If two balls are drawn without replacement, what is the probability that both are red?

Accepted Answer

$$ \frac{5}{12} 	imes \frac{4}{11} $$

Question 16

Which of the following best describes the probability of 'at least one' event occurring in a sequence of independent trials?

Accepted Answer

$$ 1 - P(	ext{none}) $$

Chapter 3: Probability – Conditional Probability and the Multiplication Rule

스터디 가이드 - 연습 문제

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