# Probability Distributions and Statistical Inference Chapter Exam

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#### Question 1 1. 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?

#### Question 2 2. When two six-sided dice are rolled, what is the probability of getting doubles? (two ones, two twos, etc.)

#### Question 3 3. 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.

#### Question 4 4. When you roll two six-sided dice, what is the probability you get a sum of 7?

#### Question 5 5. From mortality tables it has been determined that the probability of a 20-year old female non-smoker dying within the year is 0.0023. Suppose an insurance company wants to sell a $60,000 1-year term life insurance policy to a 20-year old non-smoking female. What should they charge for the policy to make a profit of $30 per policy?

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#### Question 6 6. When one event affects the outcome of another event, we call them:

#### Question 7 7. 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?

#### Question 8 8. 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?

#### Question 9 9. 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?

#### Question 10 10. 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?

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#### Question 11 11. An agency decides to conduct a survey on household incomes in their county. Let x = the household income. What type of variable is x?

#### Question 12 12. When you roll two six-sided dice, what is the probability of getting a sum of 11?

#### Question 13 13. 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?

#### Question 14 14. 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?

#### Question 15 15. 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?

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#### Question 16 16. 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?

#### Question 17 17. 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)?

#### Question 18 18. Suppose you draw two cards from a standard deck of 52. What is the probability that they are both kings?

#### Question 19 19. 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?

#### Question 20 20. 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?

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Question 21
21.
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?

#### Question 22 22. 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?

#### Question 23 23. Which of the following is NOT a property of a random variable?

#### Question 24 24. Suppose you play a game with five 6-sided dice. How many different outcomes are possible?

#### Question 25 25. 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?

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#### Question 26 26. Suppose you toss three coins, what is the probability you get three heads?

#### Question 27 27. 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?

#### Question 28 28. Suppose a die was constructed to have 10 sides of equal area (decahedron) numbered 1 through 10. And, the probability of the die landing with any one side up was 1/10. If you rolled two such dice, how many different outcomes would be possible?

#### Question 29 29. Suppose you toss a coin twice, what is the probability you get two heads in row?

#### Question 30 30. 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?

#### Probability Distributions and Statistical Inference Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!