Q: Which formula correctly expresses the multiplication rule for two dependent events A and B?

$$P(A \text{ and } B) = P(A) \cdot P(B|A)$$

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

A standard deck of 52 cards is used. What is the probability of drawing a queen, given that the first card drawn (without replacement) was a king?

Accepted Answer

$$\frac{4}{51}$$

Question 3

In a study, 72 children have a specific gene and 33 of them have a high IQ. What is the probability that a child has a high IQ, given that the child has the gene?

Accepted Answer

$$\frac{33}{72}$$

Question 4

Which of the following pairs of events are independent?

Accepted Answer

Tossing a coin and getting a head, and then rolling a die and obtaining a 6.

Question 5

If $$P(A) = 0.6$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.3$$

Question 6

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 7

The probability that a knee surgery is successful is $$0.85. $$What is the probability that all three surgeries are successful (assuming independence)?

Accepted Answer

$$(0.85)^3$$ \approx 0.614$$

Question 8

What is the probability that none of three independent knee surgeries are successful if the probability of success for one surgery is $$0.85$$?

Accepted Answer

$$(0.15)^3$$ \approx 0.003$$

Question 9

Using the complement rule, what is the probability that at least one of three independent knee surgeries is successful if the probability of failure for one surgery is $$0.15$$?

Accepted Answer

$$1 - (0.15)^3$ \approx 0.997$$

Question 10

In 2009, 93% of U.S. medical school seniors were matched to a residency position, and 82% of those were matched to one of their top two choices. What is the probability that a randomly selected senior was matched to a residency position and it was one of their top two choices?

Accepted Answer

$$(0.93)(0.82) \approx 0.763$$

Question 11

If $$P(B|A) = P(B)$$, what can you conclude about events A and B?

Accepted Answer

A and B are independent.

Question 12

A student is selected at random from a group where 30% are statistics students. What is the probability that at least one of three randomly selected students is a statistics student?

Accepted Answer

$$1 - (0.7)^3$

Question 13

Which formula correctly expresses the multiplication rule for two dependent events A and B?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) \cdot P(B|A)$$

Question 14

If the probability of an event E is $$0.3$$, what is the probability of the complement of E?

Accepted Answer

$$1 - 0.3 = 0.7$$

Question 15

A card is drawn from a standard deck. What is the probability that it is a queen and a club?

Accepted Answer

$$\frac{1}{52}$$

Conditional Probability and the Multiplication Rule (Chapter 3.2 Study Notes)

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