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# Discrete Probability Distributions Chapter Exam

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!

### Page 1

#### Question 1 1. 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?

#### Question 2 2. What is a probability formula that uses factorials to find the number of possible combinations of all the outcomes in an experiment?

#### Question 3 3. 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 4 4. Justin is conducting an experiment. He wants to know which type of pet is most preferred among 2nd graders. He asks them if they prefer dogs, cats, or hamsters. Is this a binomial experiment?

#### Question 5 5. 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?

### Page 2

#### Question 6 6. Suppose you toss a coin twice, what is the probability you get two heads in row?

#### Question 7 7. What do we call the number of successful outcomes expected in an experiment?

#### Question 8 8. Alysha is at a local library with her best friend. They've noticed a lot of cute boys in the library, and Alysha bets that of the next twenty people to enter the library, exactly 12 will be cute boys. Assuming there is a 50% chance that the next person to walk into the library is a cute boy, what is the probability that Alysha will win the bet?

#### Question 9 9. 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 10 10. Calculate the probability of getting a straight in a hand of poker.

### Page 3

#### Question 11 11. What is data that cannot be divided, is distinct, and can only occur in certain values?

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

#### Question 13 13. What is the number of successful outcomes expected in an experiment called?

#### Question 14 14. Using the table below, find the probability of 1 success out of 10 trials, with a probability of .5.

#### Question 15 15. What is the number of successes in a binomial experiment called?

### Page 4

#### Question 16 16. Jon and Alex decide to play skee ball. This game only has one ring, and the guys must roll the ball into the 10,000 point ring or they won't get any points. Each of them has a 50% chance of success with each roll and will each roll 6 balls. What is the probability that Jon will get the ball in the ring exactly 4 times?

#### Question 17 17. Which variable represents the number of trials when solving the expected value formula?

#### Question 18 18. What variable represents the probability of success on an individual trial?

#### Question 19 19. 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 20 20. Assuming that an ace counts as a one, calculate the number of combinations of straight flushes for a poker hand. (In other words, disregard the royal flush.)

### Page 5

#### Question 21 21. 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 22 22. What do we call an experiment that contains a fixed number of trials that results in only one of two outcomes: success or failure?

#### Question 23 23. What is an experiment that contains a fixed number of trials that results in only one of two outcomes: success or failure?

#### Question 24 24. When one event affects the outcome of another event, we call them:

#### Question 25 25. What is an experiment that contains a fixed number of trials that results in only one of two outcomes: success or failure?

### Page 6

#### Question 26 26. If an experiment has independent outcomes and a fixed number of trials, then what else will it need to be a binomial experiment?

#### Question 27 27. What do we call the number of successful outcomes expected in an experiment?

#### Question 28 28. 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?

#### Question 29 29. 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?

#### Question 30 30. What is the formula for binomial combinations?

#### Discrete Probability Distributions 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!

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