Name:________________________________________ Date:_________________________ Math 221 Week 5 Quiz Show as much work for partial credit!! Round all probabilities to three decimal places. Probability: 1. Two dice are rolled. We define events A, B, C and D as follows A: Getting a sum less than 7 B: Getting doubles (1-1, 2-2, etc) C: Getting two even numbers D: Getting a sum greater than 7 a) Are events A and B mutually exclusive (Disjoint)? Explain b) Are events A and D mutually exclusive (Disjoint)? Explain c) Are events B and C mutually exclusive (Disjoint)? Explain A king size bag of m&m's contains 20 red, 12 brown, 10 blue, 7 yellow, 13 green, and 17 orange. Find the following probabilities: If one is selected at random: 2. P(yellow) 3. P(Red or Orange) If three are selected in sequence, with replacement, find: 4. P(blue and green and brown) If four are selected in sequence, without replacement, find: 5. P(orange and red and blue and blue) A student survey of science majors at a state university yielded the results below. Use the summarized table to answer the questions that follow. Biology Male Female Total Chemistry Majors Physics 220 245 465 173 123 296 102 58 160 Earth Science 38 41 79 Total 533 467 1000 If one of the 1000 students is randomly selected, find the following probabilities: (Round to three significant digits) 6. P(Biology Major) = 7. P(Female and Chemistry Major) = 8. P(Male or Earth Science Major) = 9. P(Physics Major or Chemistry Major) = 10. P(Biology | Male) = 11. P(Not a Biology Major) 12. Are the events Male and Biology mutually exclusive? Explain. Counting Rules (Factorials, Permutations, and Combinations) 13. A restaurant has 7 kinds of appetizers to choose from, 10 kinds of main courses, 5 kinds of desserts, and 4 kinds of drinks. If a customer selects one item from each of these four categories, how many different outcomes are possible? 14. A manager at a car dealership has 6 new cars to place in the showroom. How many different ways can she put the cars in order? 15. A jury pool has been narrowed down to 11 people, of which 6 will be randomly selected. How many ways are possible to select these 6 jurors? Probability Distributions 16. Debit Card Transactions: A bank recorded the number of debit card transactions made by its customers in one day. Then number x of daily debit card transactions per customer can be approximated by the following probability distribution. Use Statcrunch to answer the questions that follow: X P(X) 0 0.22 1 0.28 2 0.20 3 0.12 4 0.09 5 0.07 6 0.02 Find: (Round answers to 2 decimal places and include units) a. The mean (expected value) number of daily debit card transaction. b. The standard deviation for number of daily debit card transactions. Discrete Distributions (Binomial, Poisson, and Geometric) 17. 55% of all small businesses in the United States have a website. You randomly select 12 small businesses. Let x be a binomial random variable denoting the number of small businesses out of 12 that have a website. Use statcrunch to find the following probabilities. a. Find n and p b. Find the probability that exactly 7 of the businesses will have a website. c. Find the probability that at least five of the businesses will have a website. d. Find the probability that less than four of the businesses will have a website. e. Find the probability that between 6 and 11 (inclusive) of the businesses will have a website. f. Find the mean and standard deviation for the number of businesses that will have a website. 18. A commuter airline receives a mean of 7.6 complaints per day from its passengers. Using the Poisson distribution and statcrunch, find the following probabilities: a. Find the probability that on a certain day this airline will receive exactly 6 complaints. b. Find the probability that on a certain day this airline will receive at most 4 complaints. c. Find the probability that on a certain day this airline will receive more than 5 complaints. d. Find the probability that on a certain day this airline will receive between 4 and 7 (inclusive) complaints. 19. Over a very long period of time, it has been noted that on Friday's 32% of the customers at the drive-in window at the bank make deposits. Recall that for the Geometric distribution you cannot use statcrunch to find probabilities. Instead use the website and directions that I gave you in your week 4 notes. a. What is the probability that it takes 3 customers at the drive-in window before the first one makes a deposit? b. What is the probability that the first deposit made will be on the 1st, 2nd, or 3rd person to go through the drive through? c. What is the probability that the first deposit made will NOT be made on the 1st, 2nd, or 3rd person to go through the drive through