Question 1

A standard deck of 52 playing cards is shuffled, and one card is drawn at random. What is the probability of drawing a club?

Accepted Answer

$$ \frac{1}{4} $$

Question 2

Suppose you roll a fair six-sided die. Let event A be 'rolling at least a 3.' What is the complement of event A?

Accepted Answer

Rolling a 1 or 2

Question 3

In a recent year, there were about 3,000,000 skydiving jumps and 21 of them resulted in death. Using the relative frequency approach, what is the probability of dying in a skydiving jump?

Accepted Answer

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

Question 4

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

Accepted Answer

As the number of trials increases, the relative frequency probability of an event approaches the actual probability.

Question 5

A jar contains 12 slips of paper, each with a different month of the year written on it. What is the probability of randomly drawing a slip with a month that has exactly four letters?

Accepted Answer

$$ \frac{3}{12} $$

Question 6

Which of the following is NOT a requirement for using the classical approach to probability?

Accepted Answer

The event must be subjective.

Question 7

If the actual odds against an event A are 7:3, what is the probability of event A occurring?

Accepted Answer

$$ \frac{3}{10} $$

Question 8

A casino offers a game where the probability of winning is $$ \frac{1}{38} . $$The casino pays $$35 for every 1 $$bet if you win. What are the payoff odds against winning?

Accepted Answer

35:1

Question 9

Which of the following is an example of a subjective probability?

Accepted Answer

Estimating the chance of rain tomorrow based on your own experience and weather knowledge.

Question 10

If the probability of an event A is $$0.2$$, what is the probability of the complement of A?

Accepted Answer

$$0.8$$

Question 11

A lottery has 1000 tickets, and only one ticket wins the grand prize. What are the actual odds against winning the grand prize with one ticket?

Accepted Answer

999:1

Question 12

A student claims that because there are two possible outcomes (pass or fail) on a test, the probability of passing is $$0.5. $$What is wrong with this reasoning?

Accepted Answer

The outcomes are not necessarily equally likely.

Question 13

If you bet $10 on a roulette number with actual odds against winning of 37:1, and the casino pays you according to the actual odds, what is your net profit if you win?

Accepted Answer

$$370$$

Question 14

Which of the following best describes a simple event?

Accepted Answer

An outcome that cannot be broken down into simpler components.

Question 15

A coin is tossed three times. What is the size of the sample space?

Accepted Answer

8

Question 16

If the probability of an event A is $$0.25$$, what are the actual odds in favor of A?

Accepted Answer

1:3

Question 17

A medical test for a rare disease has a 99% chance of correctly identifying a sick patient (true positive) and a 95% chance of correctly identifying a healthy patient (true negative). If 1 in 1000 people actually have the disease, which approach would best estimate the probability that a randomly selected person tests positive?

Accepted Answer

Classical approach is not appropriate; use relative frequency or simulations.

Question 18

If you conduct an experiment and observe that event A occurs 40 times out of 200 trials, what is the relative frequency probability of event A?

Accepted Answer

$$ \frac{40}{200} = 0.2 $$

Question 19

A casino game has a probability of winning of $$ \frac{1}{20} . $$The casino offers a payoff of $$18 for every 1 $$bet. What is the casino's expected net profit per $1 bet, assuming the actual odds are used?

Accepted Answer

$$1$$

Question 20

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

Accepted Answer

It applies to the behavior over many trials, not to individual outcomes.

Chapter 4: Probability – Basic Concepts and Applications

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