2. Random Probability Distributions BinomialMultinomial Hyper- geometric 10 20 30 40 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10

3. Topic 1 – 10 Points QUESTION: What are the 2 requirements to be a probability distribution? ANSWER: The sum of the probabilities of an event must =1 and the probability for each sample is equal to 0 and 1.

4. Topic 1 – 20 Points QUESTION: Which distribution is divided into success or failures? ANSWER: A binomial distribution

5. Topic 1 – 30 Points QUESTION: Which types of distributions have only 2 possible outcomes? ANSWER: Binomial & Hypergeometric

6. Topic 1 – 40 Points QUESTION: Name the 4 main formulas used for all probability distributions and how to calculate them ANSWER: Mean, Variance, Standard Deviation, and Expectation

7. Topic 1 – 50 Points QUESTION: Create a probability distribution table for a family with 3 children, let X be the number of girls. ANSWER: X0123 P(X)1/83/8 1/8

8. Topic 2 – 10 Points QUESTION: How many possible outcomes are there in a binomial distribution ANSWER: 2

9. Topic 2 – 20 Points QUESTION: When calculating the probability for a binomial distribution, what are all the variables and what do they stand for? ANSWER: p for probability of success, q for probability of failure, n is the number of trials, and X is the number of successes

10. Topic 2 – 30 Points QUESTION: A survey found that one out of five Americans say he or she has visited a doctor in any given month. If 10 people are selected at random, find the probability that exactly 3 will have visited the doctor last month. ANSWER:.201

11. Topic 2 – 40 Points QUESTION: Find the mean, variance, and standard deviation if a coin is flipped 4 times. ANSWER: Mean = 2, Variance = 1, Standard Deviation = 1

12. Topic 2 – 50 Points QUESTION: If 30% of people in a community use the library in one year, find the probability that at least 5 used the library out of a sample of 15 people. ANSWER:.485

13. Topic 3 – 10 Points QUESTION: Can the formula for finding the probability of multinomial distributions be used for binomial distributions? If so, why? ANSWER: Yes, since a binomial distribution is a special case of a multinomial distribution.

14. Topic 3 – 20 Points QUESTION: State the formula for finding the probability of a multinomial distribution. ANSWER:

15. Topic 3 – 30 Points QUESTION: A bag contains 4 white balls, 3 red calls, and 3 blue balls. A ball is selected at random. If it is replaced each time, find the probability that if 5 balls are selected, 2 are white, 2 are red, and 1 is blue. ANSWER: 81/625

16. Topic 3 – 40 Points QUESTION: Use the multinomial formula to find the probability using these numbers. N=5, X 1 =1, X 2 =2, X 3 =2, p 1 =.3, p 2 =.6, p 3 =.1 ANSWER:.0324

17. Topic 3 – 50 Points QUESTION: The probability that a person will make 0, 1, 2, or 3 errors on his or her income tax return is.5,.3,.15, and.05, respectively. If 30 claims are selected, find the probability that 15 will contain no errors, 8 will contain 1 error, 5 will contain 2 errors, and 2 will contain 3 errors. ANSWER: 0.008

18. Topic 4 – 10 Points QUESTION: What is the biggest difference between this distribution compared to binomial or multinomial distributions? ANSWER: It is dependent

19. Topic 4 – 20 Points QUESTION: Write the formula for the probability of an event in a hypergeometric distribution ANSWER:

20. Topic 4 – 30 Points QUESTION: Ten people apply for a job to be the assistant manger at Berrigans in Bloomsburg. Five have completed college and 5 have not. If the manager selects three applicants at random, find the probability that all three are college graduates. ANSWER: 1/12

21. Topic 4 – 40 Points QUESTION: Suppose a researcher goes to a small college with a faculty of 200, 12 of which have a blood type O- negative. She obtains a sample of 20 of the staff. If X represents the staff with a blood type ) negative, what is the probability of 3 have that blood type? ANSWER:.0833

22. Topic 4 – 50 Points QUESTION: Suppose a researcher goes to a small college with a faculty of 200, 12 of which have a blood type O- negative. She obtains a sample of 20 of the staff. If X represents the staff with a blood type ) negative, what is the probability that at least 1 has a blood type O- negative? ANSWER:.7282

23. Topic 5 – 10 Points QUESTION: What are the three types of distributions we went over in class? ANSWER: Binomial, Multinomial, and Hypergeometric

24. Topic 5 – 20 Points QUESTION: Which probability distribution is this formula used for? ANSWER: Binomial Distributions

25. Topic 5 – 30 Points QUESTION: What is a variable whose values are determined by chance? ANSWER: A random variable

26. Topic 5 – 40 Points QUESTION: A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold at $3 each. Find the expectation if a person buys a ticket. ANSWER: -$1.00

27. Topic 5 – 50 Points QUESTION: In the textbook, there was one type of distribution we did not go over, what was it called? ANSWER: A Poisson Distribution