Q: If two events $$A$$ and $$B$$ are independent, what is the probability that both occur?

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

Question 1

Which of the following best describes a simple event in probability?

Accepted Answer

An outcome or event that cannot be further broken down into simpler components.

Question 2

Given three births, which of the following is NOT a simple event?

Accepted Answer

The event '2 girls and 1 boy'.

Question 3

If a procedure has $$n$$ equally likely simple events and event $$A$$ can occur in $$s$$ different ways, what is the classical probability of event $$A$$?

Accepted Answer

$$P(A) = \frac{s}{n}$$

Question 4

A survey of 2003 adults found that 366 said they have seen a ghost. What is the probability that a randomly selected adult from this survey has seen a ghost? (Round to three significant digits)

Accepted Answer

$$P = \frac{366}{2003} = 0.183$$

Question 5

Which approach to probability is most appropriate when outcomes are not equally likely and historical data is available?

Accepted Answer

Relative frequency approximation

Question 6

If $$P(A) = 0.87$$ for a household having a smartphone, what is the probability that a randomly selected household does NOT have a smartphone?

Accepted Answer

$$P = 0.13$$

Question 7

Which of the following statements about the Law of Large Numbers is correct?

Accepted Answer

It states that as a procedure is repeated, the relative frequency probability approaches the actual probability.

Question 8

If the probability of an event is 0, what does this mean?

Accepted Answer

The event is impossible.

Question 9

What is the probability of the complement of event $$A if$$ $$P(A) = 0.25$$?

Accepted Answer

$$P(\overline{A}) = 0.75$$

Question 10

A casino offers a bet with payoff odds of 35:1 on a $5 bet. What is the net profit if you win?

Accepted Answer

$$175$$

Question 11

If the probability of a hard drive failing in a year is $$0.0289$$, what is the probability that two independent hard drives both fail in a year?

Accepted Answer

$$(0.0289)^2 = 0.000835$

Question 12

Which of the following is true about disjoint (mutually exclusive) events?

Accepted Answer

They do not overlap and cannot occur together.

Question 13

Using the addition rule, what is $$P(A 	ext{ or } B) if$$ $$P(A) = 0.3$$, $$P(B) = 0.5$$, and $$P(A 	ext{ and } B) = 0.1$$?

Accepted Answer

$$0.3 + 0.5 - 0.1 = 0.7$$

Question 14

If two events $$A$$ and $$B$$ are independent, what is the probability that both occur?

Accepted Answer

$$P(A 	ext{ and } B) = P(A) 	imes P(B)$$

Question 15

A drug test yields a positive result with probability $$0.042. If $$three employees are randomly selected (without replacement) from a population of 130,639,273, what is the probability all three test positive? (Use the 5% guideline for cumbersome calculations.)

Accepted Answer

$$(0.042)^3 = 0.0000741$

Question 16

Which of the following is a correct interpretation of a probability value of $$0.001$$?

Accepted Answer

The event rarely occurs.

Question 17

If the probability of an event is $$0.05 or $$less, what can be said about the event in the context of inferential statistics?

Accepted Answer

It is considered a significantly rare event.

Question 18

Which of the following is NOT a valid approach to finding probability?

Accepted Answer

Guessing without any information

Question 19

A simulation is most useful in probability when:

Accepted Answer

None of the standard approaches can be used.

Chapter 4: Probability – Basic Concepts and Approaches

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