Q: Which of the following is the correct formula for the payoff odds against event $$A$$?

$$\text{Payoff odds against event } A = \frac{\text{net profit}}{\text{amount bet}}$$

Question 1

Which of the following best describes a simple event?

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

What is the probability of guessing correctly on a True-False question?

Accepted Answer

$$0.5$$

Question 4

If a couple plans to have four children, and each child is equally likely to be a boy or a girl, how many outcomes are in the sample space for the gender of the children (in order of birth)?

Accepted Answer

$$16$$

Question 5

Which of the following probabilities is closest to 'certain' on the probability scale?

Accepted Answer

$$1$$

Question 6

When rounding a probability value, which of the following is the recommended approach?

Accepted Answer

Round to three significant digits or give the exact fraction/decimal.

Question 7

A litter of 3 puppies can be either solid brown (B) or spotted (S). How many outcomes are in the sample space for the coloring of the puppies (in order of birth)?

Accepted Answer

$$8$$

Question 8

If the probability of winning a bet is $$\frac{1}{38}$$, what are the actual odds against winning?

Accepted Answer

$$37:1$$

Question 9

If you bet $$5 on the number 13 in roulette and win, with payoff odds of 35$$:1$, how much net profit do you make?

Accepted Answer

$$175$$

Question 10

If the casino changed the payoff odds to match the actual odds against winning on 13 in roulette ($$37:1$$), how much would you win on a $$5$$ bet if the outcome were 13?

Accepted Answer

$$185$$

Question 11

Which of the following best describes the sample space for rolling a single six-sided die?

Accepted Answer

$$\{1, 2, 3, 4, 5, 6\}$$

Question 12

If Thanksgiving Day in the United States can fall on either a Wednesday or a Thursday, and each day of the week is equally likely, what is the probability that Thanksgiving falls on a Wednesday or Thursday?

Accepted Answer

$$\frac{2}{7}$$

Question 13

Which of the following is the correct formula for the payoff odds against event $$A$$?

Accepted Answer

$$	ext{Payoff odds against event } A = \frac{	ext{net profit}}{	ext{amount bet}}$$

Question 14

If an event is described as 'impossible,' what is its probability?

Accepted Answer

$$0$$

Question 15

Which of the following is an example of an event, but NOT a simple event?

Accepted Answer

Getting 2 girls and 1 boy in three births.

Question 16

If you select a day at random from September, what is the probability that the day is a prime number (assuming September has 30 days)?

Accepted Answer

$$\frac{10}{30}$$

Question 17

Which of the following best describes the actual odds in favor of event $$A if $$the odds against $$A$$ are $$a:b$$?

Accepted Answer

$$b:a$$

Probability and Sample Spaces: Study Notes for Statistics Chapter 4.1

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