Chapter 6: Probability

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1 Chapter 6: Probability Name 1. At Beth & Mary's Ice Cream Emporium customers always choose one topping to sprinkle on their ice cream. The toppings are classified as either candy (C) or fruit (F) toppings. Consider the chance experiment where the choice of toppings -- (C) or (F) -- is recorded for each of the next two customers who order ice cream. a) List all the events in the sample space. b) Using your sample space in part (a), list the outcomes for each of the following events A = the event that both customers pick candy B = the event that both customers pick the same type of topping C = the event that at least one customer picks a candy topping A: B: C: c) Display the sample space in the form of a tree diagram. Page 1 of 9

2 2. First graders at an elementary school were classified according to whether they were first born or not, and also whether both parents worked outside the home. This resulted in the accompanying table. First Born Older Siblings Both work outside home At least one parent does not work outside home 8 25 Suppose that one of these students is selected at random. Define events A, B, and C as follows: A = the event that the selected student is a first born B = the event that the selected student's parents both work outside the home C = the event that the selected student has older siblings For each pair of events in the following table, indicate whether the two events are disjoint and/or independent by putting a Y or N in the appropriate cells. Y = Yes, N = No A, B B, C A, C Disjoint Independent Page 2 of 9

3 3. The diamond python (Morelia spilota), an Australian snake, is about 3 feet long as an adult. In a multi-year study of the habitats of these creatures, 997 were captured. The following table displays the capture locations of these snakes by season of the year and habitat. The "other" category includes trees, logs, rocks, open ground, and under filtering cover such as shrubs. Suppose a diamond python is selected at random from the study records. Diamond Python Habitat Buildings Other Total Spring Summer Autumn Winter Total Suppose a diamond python is selected at random from the study records. Calculate the probability that: a) The selected diamond python was located in a building, given that it was spring. b) The selected diamond python was located other than in a building given that it was spring or summer. c) The selected diamond python was observed in a building in the summer. Page 3 of 9

4 4. In November 2002, Janet Napolitano, a Democrat, was elected Governor of Arizona, defeating Republican Matt Salmon and Independent Richard Mahoney. This was a somewhat surprising outcome, since there are more registered Republicans than Democrats in the state. The table below presents data from a survey of a sample of voters in the election. The number who voted for each of the candidates is presented in the rows, and the party affiliation of the voters is presented in the columns. Suppose that one of these voters is selected at random. Use the information in the table to answer the questions below. Be sure to define and use appropriate notation. Voters who are registered as Voted for D R I Totals Napolitano (D) Salmon (R) Mahoney (I) Totals a) What is the probability that the selected voted for Napolitano? b) What is the probability that the selected voter is a registered Democrat? Page 4 of 9

5 c) What is the probability that the selected voter cast a vote for Napolitano, given that the selected voter is a Democrat? d) A local reporter, commenting on this election, said, "Napolitano won because she attracted a larger share of crossover voters." (A crossover voter is one who has a party affiliation but votes differently than his or her party affiliation). What is the probability that the selected voter cast a vote for Napolitano, given that he or she is a crossover voter? Page 5 of 9

6 5. All statistics teachers love Girl Scout Cookies. The number of boxes of Girl Scout cookies a statistics teacher orders is (of course) determined by the roll of a 4-sided fair die. If a one appears, 6 boxes are ordered; if any other number appears, 2 boxes are ordered. a) What is the probability that a statistics teacher places an order for 2 boxes of Girl Scout cookies? b) What is the probability that two statistics teachers (each rolling a die to determine the number of boxes ordered) will each order 6 boxes each? c) What is the probability that for two statistics teachers (each rolling a die to determine the number of boxes ordered), the first will order 6 boxes and the second will order 2 boxes? d) What is the probability that for two statistics teachers (each rolling a die to determine the number of boxes ordered), exactly one will order 6 boxes? Page 6 of 9

7 6. Like many professionals, the clergy in mainline Protestant churches have pension plans. Due to the nature of the ministry, investment strategies may involve what are known as screens. Screens are rules that prevent a pension fund administrator from investing in corporations that are involved with, for example, alcohol, gambling, tobacco and weapons of mass destruction. Ministers may elect to invest in two broad categories: regular and social purpose funds, which would typically use screens in their investment strategy. The use of screens may reduce their monthly benefit at retirement. The data below are from a survey of ministers about their support in principle for the use of such screens. They were asked if the screens should be applied to the regular funds, the social purpose funds, both, or neither. The ministers were classified by the current percentage of their investments in the social purpose funds: 0%, 10 59%, 60% or greater. Support in principle for using screens Use screens for: 0% group 10-59% group 60+% group Total Social purpose funds only Both social purpose and regular funds Neither Uncertain Total a) What is the probability that a minister selected at random from those who participated in the survey was uncertain about the use of screens? Page 7 of 9

8 b) What is the probability that a minister selected at random from those who participated in the survey was in the 60+ group and supported the use of screens for social purpose funds only? c) What is the probability that a minister selected at random from those who participated in the survey felt the screens should be used for social purpose funds only or for both social purpose and regular funds, given that they were in the 10-59% group? d) What is the probability that a randomly selected uncertain minister would be in the 0% group? Page 8 of 9

9 7. Three of the most common pets are cats, dogs, and fish. Many families have more than one type of pet, and some have all three! Define the following events, with the probabilities given. (The fish-and-cats combination doesn't seem too popular!) F = a family has at least one pet fish : P(F) = 0.20 D = a family has at least one pet dog: P(D) = 0.32 C = a family has at least one pet cat: P(C) = 0.35 PF ( Ç D) = 0.18; PF ( Ç C) = 0.07; PD ( C) = 0.30 Suppose that a family is selected at random. Calculate each of the following (show your work): a) PF ( D ) b) PF ( È D) c) PC ( Ç D) Page 9 of 9

Chapter 6: Probability

Chapter 6: Probability Name 1. A small ferryboat transports vehicles from one island to another. Consider the chance experiment where the type of vehicle -- passenger (P) or recreational (R) vehicle --