Q: A drug test has 45 positive and 5 negative results among 50 drug users. If two subjects are selected with replacement, what is the probability the first is positive and the second is negative?

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

Q: If $$P(B|A) = 0.7$$ and $$P(A) = 0.4$$, what is $$P(A \text{ and } B)$$?

$$P(A) \times P(B|A) = 0.4 \times 0.7 = 0.28$$

Question 1

A recent study found that out of 3,000,000 skydiving jumps, 21 resulted in death. What is the probability of dying during a skydiving jump? (Round your answer to six decimal places.)

Accepted Answer

$$\frac{21}{3,000,000} = 0.000007$$

Question 2

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 3

A sample of 8,505 high school drivers found that 3,785 texted while driving in the past 30 days. What is the probability that a randomly selected driver texted while driving?

Accepted Answer

$$\frac{3785}{8505} = 0.445$$

Question 4

Which of the following best describes the Law of Large Numbers?

Accepted Answer

As a procedure is repeated many times, the relative frequency probability of an event approaches the actual probability.

Question 5

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

Accepted Answer

$$P(A) + P(B) = 0.3 + 0.5 = 0.8$$

Question 6

A clinical trial randomly selects a subject. Event A: subject is male. Event B: subject is female. What is true about events A and B?

Accepted Answer

They are disjoint (mutually exclusive) events.

Question 7

If $$P(A) = 0.4$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.2$$, what is $$P(A 	ext{ or } B)$$?

Accepted Answer

$$0.4 + 0.5 - 0.2 = 0.7$$

Question 8

A drug test has 45 positive and 5 negative results among 50 drug users. If two subjects are selected with replacement, what is the probability the first is positive and the second is negative?

Accepted Answer

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

Question 9

If $$P(B|A) = 0.7$$ and $$P(A) = 0.4$$, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$P(A) 	imes P(B|A) = 0.4 	imes 0.7 = 0.28$$

Question 10

A test for a disease has a false positive rate of $$0.013. $$Who would suffer from a false positive result?

Accepted Answer

A person who does not use drugs but tests positive.

Question 11

If $$P(A) = 0.25$$, what is $$P(\overline{A})$$?

Accepted Answer

$$1 - 0.25 = 0.75$$

Question 12

In a population, 10% of adults use drugs. If three adults are randomly selected with replacement, what is the probability all three use drugs?

Accepted Answer

$$(0.10)^3 = 0.001$

Question 13

Which of the following is an example of independent events?

Accepted Answer

Flipping a coin and rolling a die.

Question 14

A study finds the probability of a rare disease in a population is $$0.0005. If a $$screening test is positive in 0.05 of cases, is this a significantly high result?

Accepted Answer

Yes, because $$0.05 is $$considered a threshold for significance.

Question 15

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

Accepted Answer

$$0.6 	imes 0.5 = 0.3$$

Question 16

Which of the following best describes a compound event?

Accepted Answer

An event that combines two or more simple events.

Question 17

If the odds in favor of an event are $$3:7$$, what is the probability of the event?

Accepted Answer

$$\frac{3}{3+7} = 0.3$$

Question 18

A population has a death rate of 8 per 1000 people in a year. What is the probability that a randomly selected person from this population dies in that year?

Accepted Answer

$$\frac{8}{1000} = 0.008$$

Chapter 4: Probability – Structured Study Notes for Statistics Students

Guida di studio - Domande di pratica

Study guide - Flashcard