HS STATS CH.6

From mortality tables it has been determined that the probability of a 20-year old male non-smoker dying within the year is 0.0035. Suppose an insurance company wants to sell a $50,000 1-year life insurance policy to a 20-year old non-smoking male. What should they charge for the policy to break even?

$175

You play a game with two six-sided dice. If you roll a sum of 6 or 8, you win $3. If you roll a sum of 11, you win $1, but for anything else, you lose $2. If you continue to play this game, what do you expect to win in the long run?

-$0.44 per roll

Suppose you play a game with two six-sided dice, where if you get doubles, you win $10, but for anything else you lose $5. If you continue to play this game, how much do you expect to win or lose per roll in the long run? In other words, what is the expected value of this game?

-$2.50

Consider the following probability distribution (see table below) of the number of firearms in a household, constructed from a survey of 25,000 randomly selected households. Let X = the number of firearms in a household, and assume that the probability of a household having more than 6 firearms in the home is negligible. If a household is selected at random, then how many firearms would you expect them to have?

0.468

Vickie is playing a lottery where she will choose 3 numbers between 1 and 25. No numbers are repeated and the order of the numbers does not matter. What are her chances of picking the winning combination of numbers?

1 in 2,300

Naomi is buying a ticket for the lottery. She can pick 5 numbers, 1 through 15, with no numbers repeating. Order does not matter for her to win. What are her chances of winning?

1 in 3,003

Hannah is playing the lottery. She can pick 5 numbers between 1 and 32, with no numbers repeating. The order of these numbers does not matter. She can also pick a bonus number between 1 and 20. What are her chances of picking all of the numbers, including the bonus, correctly?

1 in 4,027,520

What is the chance of rolling a 3 on any given six-sided die?

1 in 6

A television channel conducts a study on the number of TVs per household in their service area. Out of 1000 households surveyed, 350 have one TV, 500 have two TVs, 120 have three TVs and 30 have four TVs. How many TVs does each household have on average?

1.83

When you roll two six-sided dice, what is the probability of getting a sum of 11?

1/18

Suppose you draw two cards from a standard deck of 52. What is the probability that they are both kings?

1/221

When two six-sided dice are rolled, what is the probability of getting doubles? (two ones, two twos, etc.)

1/6

Suppose you toss three coins. What is the probability that you get two heads and one tail if the order in which you get them does not matter?

3/8

Asia is conducting an experiment for her psychology class. She asks 80 students if they believe in hypnosis. Previous studies show that 60% of the population believes in hypnosis. Based on the expected value, how many people should answer yes, they do believe in hypnosis, in Asia's study?

48 people

Say you're playing Blackjack, and you have a four and a jack. If you see that one of the dealer's two cards is a five, then what's the probability that you will be dealt a card that helps you?

54%

Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. Let X = the number of firearms in a household. From the survey of 30,000 households it was determined that the empirical probability of X = 1 was 0.2. How many of the households in the survey had one firearm in their home?

6,000

Suppose a survey was conducted across the country regarding the number of firearms that people had in their households. If the sample size was 25,000 and 17,000 households reported that they had no firearms in their home, what would be the empirical probability that a randomly selected household had no firearms in their home?

68%

A game of Blackjack is played. Suppose you are the first player dealt with a new pack of cards. What is the probability you get an ace and a jack (in any order)?

8/663

A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). On one spin of the roulette wheel, what is the probability that the ball lands on a red slot?

9/19

What is game theory?

A field of analysis used to guide logical decision-making.

Which of the following is NOT a property of a random variable?

A random variable cannot be negative.

Why would a person who has few wrecks benefit from a lower premium?

Because even though a low premium comes with a high deductible, if the driver has a low chance of a wreck, they're less likely to ever need to pay the deductible.

Why would height be defined by a continuous random variable?

Because there is an infinite spectrum of possible heights

19 Why is the result of rolling a die considered a discrete random variable?

Because when you roll a die, there is a countable number of possible outcomes.

What is a probability formula that uses factorials to find the number of possible combinations of all the outcomes in an experiment?

Combination formula

When one event affects the outcome of another event, we call them:

Dependent events

What do we call data that cannot be divided, which is distinct, and can only occur in certain values?

Discrete data

You conduct an experiment where you want to measure the number of rolls it takes to get two 6's in a row when you roll a fair six-sided die. State whether the random variable is discrete or continuous and give a summary of its values

Discrete with values 2, 3, 4, 5, 6, etc.

What do we call the number of successful outcomes expected in an experiment?

Expected value

For which of the following random processes would you define a discrete random variable?

Flipping coins

Suppose you play a game where you spin a spinner (see picture below) with areas of the colors on the spinner broken down as shown: 10% blue, 60% green, and 30% red. In addition, if the spinner lands on red you win 6 points, if it lands on blue you win 1 point, and if it lands on green you lose 5 points. If you keep spinning, how many points can you expect to win or lose per game?

I expect to lose 1.1 points per game.

You play a game where you toss a coin. On each toss if it lands with heads up, you win $1. However, if it lands with tails up, you lose $2. If you continue to play this game, how much can you expect to win or lose per game?

I expect to lose 50 cents per game.

A roulette wheel has 38 slots labeled with the numbers 1 through 36 and then 0 and 00. Slots 1 through 36 are colored either red or black. There are 18 red and 18 black. Slots 0 and 00 are colored green (see picture). Suppose that for a bet of $1 on red, the casino will pay you $2 if the ball lands on a red slot (a net gain of $1), and otherwise you lose your dollar. What can you expect to win or lose in this game?

I expect to lose about 5 cents per game.

Solving for the expected value of a continuous probability distribution involves which of the following?

Integration

Which of the following is TRUE regarding the expected value associated with the probability density function?

It can be thought of as the long term-average value of the probability distribution.

At a particular casino, you pay $1 to play a hand of Blackjack. If you get a total of 21 in your first two cards, then you win $10. If not, you lose your dollar. If you are the only one playing this game, then how much do you expect to win or lose per hand?

Lose $0.52 per hand

Suppose you play a game with two 4-sided dice with sides numbered 1 through 4. If you roll a sum of 8 (face down), you win $10. If you roll anything else, you lose $1. What can you expect to win or lose in this game?

Lose 31 cents per game

What variable represents the number of trials in an experiment?

N

What variable represents the probability of success on an individual trial?

P

A continuous probability distribution function is also known as which of the following?

Probability density function

What do we call a graph of probabilities associated with all the possible values taken by a continuous random variable?

Probability density function

In a probability distribution function, what does the x-axis typically represent?

The possible values the random variable can take

In a probability distribution function, what does the y-axis typically represent?

The probability of each outcome

What are expected values?

The results we can anticipate given that a particular event occurs

Which of the following is associated with a continuous random variable?

Weight measurements within a population

You decide to conduct a survey of families with two children. You are interested in counting the number of boys (out of 2 children) in each family. Is this a random variable, and if it is, what are all its possible values?

Yes, it is a random variable, and its values are 0, 1, or 2.

A game is played where you draw two cards from a deck of 52 cards. If the cards are both jacks, then you win $5. Otherwise you lose $1. If you play this game, then what can you expect to win or lose in the long run?

lose $0.97 per game

An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x?

x is a continuous random variable.

You decide to collect a bunch of cans of soda and measure the volume of soda in each can. Let x = the number of mL of soda in each can. What type of variable is x?

x is a continuous random variable.