Q: Suppose you randomly select a person from a population. Let event A be 'the person is a male' and event B be 'the person is a female.' What is the probability that the person is either a male or a female?

$$P(A \text{ or } B) = P(A) + P(B)$$

Q: Which formula is used to find the probability that either event A or event B occurs (or both)?

$$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$$

Q: Two subjects are randomly selected with replacement from a group of 50, where 45 have positive test results and 5 have negative test results. What is the probability that the first selected subject has a positive result and the second has a negative result?

$$\dfrac{45}{50} \times \dfrac{5}{50} = 0.09$$

Q: If two subjects are selected without replacement from the same group (45 positive, 5 negative out of 50), what is the probability that the first is positive and the second is negative?

$$\dfrac{45}{50} \times \dfrac{5}{49} \approx 0.0918$$

Question 1

Which of the following statements best describes disjoint (mutually exclusive) events?

Accepted Answer

Disjoint events are events that cannot occur at the same time.

Question 2

Suppose you randomly select a person from a population. Let event A be 'the person is a male' and event B be 'the person is a female.' What is the probability that the person is either a male or a female?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B)$$

Question 3

If $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.1$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.3 + 0.5 - 0.1 = 0.7$$

Question 4

Which formula is used to find the probability that either event A or event B occurs (or both)?

Accepted Answer

$$P(A 	ext{ or } B) = P(A) + P(B) - P(A 	ext{ and } B)$$

Question 5

A clinical trial randomly selects a participant. Event A is 'the participant is taking a statistics course.' Event B is 'the participant is female.' Which statement is true?

Accepted Answer

Events A and B are not disjoint.

Question 6

If the probability that a randomly selected person has sleepwalked is $$0.292$$, what is the probability that a randomly selected person has not sleepwalked?

Accepted Answer

$$1 - 0.292 = 0.708$$

Question 7

Which of the following best describes independent events?

Accepted Answer

The occurrence of one event does not affect the probability of the other.

Question 8

Two subjects are randomly selected with replacement from a group of 50, where 45 have positive test results and 5 have negative test results. What is the probability that the first selected subject has a positive result and the second has a negative result?

Accepted Answer

$$\dfrac{45}{50} 	imes \dfrac{5}{50} = 0.09$$

Question 9

If two subjects are selected without replacement from the same group (45 positive, 5 negative out of 50), what is the probability that the first is positive and the second is negative?

Accepted Answer

$$\dfrac{45}{50} 	imes \dfrac{5}{49} \approx 0.0918$$

Question 10

When sampling without replacement from a large population, under what condition can the selections be treated as independent?

Accepted Answer

When the sample size is no more than 5% of the population.

Question 11

Three adults are randomly selected without replacement from a population of 247,436,830, where 10% use drugs. What is the probability that all three use drugs?

Accepted Answer

$$(0.10)^3 = 0.001$

Question 12

A modern aircraft has three independent hydraulic systems, each with a probability of failure of $$0.002$$ per flight. What is the probability that all three systems fail during a flight?

Accepted Answer

$$(0.002)^3 = 0.000000008$

Question 13

Using the principle of redundancy, what is the probability that flight control is maintained in the Airbus 310 with three independent hydraulic systems, each with a failure probability of $$0.002$$?

Accepted Answer

$$1 - 0.000000008 = 0.999999992$$

Question 14

Which rule should be used to find the probability that both event A and event B occur?

Accepted Answer

Multiplication Rule

Question 15

If $$P(A) = 0.4$$ and $$P(B|A) = 0.5$$, what is $$P(A 	ext{ and } B)$$ using the multiplication rule?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 16

Which of the following is a correct application of the complement rule?

Accepted Answer

$$P(A) = 1 - P(A)$$

Question 17

A system has two independent components, each with a probability of working of $$0.95. $$What is the probability that at least one component works?

Accepted Answer

$$1 - (1 - 0.95)^2$ = 0.9975$$

Question 18

Which of the following scenarios describes dependent events?

Accepted Answer

Drawing two cards from a deck without replacement.

Addition and Multiplication Rules in Probability

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