# 109 suppose that you randomly draw two cards one at a

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109.Suppose that you randomly draw two cards, one at a time,with replacement.LetG1= first card is greenLetG2= second card is greena.Draw a tree diagram of the situation.b.FindP(G1ANDG2).c.FindP(at least one green).d.FindP(G2|G1).e.AreG2andG1independent events? Explain why or why not.218Chapter 3 | Probability TopicsThis OpenStax book is available for free at
110.Suppose that you randomly draw two cards, one at a time,without replacement.G1= first card is greenG2= second card is greena.Draw a tree diagram of the situation.b.FindP(G1ANDG2).c.FindP(at least one green).d.FindP(G2|G1).e.AreG2andG1independent events? Explain why or why not.Use the following information to answer the next two exercises.The percent of licensed U.S. drivers (from a recent year)that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Ofthe licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.111.Complete the following.a.Construct a table or a tree diagram of the situation.b.FindP(driver is female).c.FindP(driver is age 65 or over|driver is female).d.FindP(driver is age 65 or over AND female).e.In words, explain the difference between the probabilities in part c and part d.f.FindP(driver is age 65 or over).g.Are being age 65 or over and being female mutually exclusive events? How do you know?112.Suppose that 10,000 U.S. licensed drivers are randomly selected.a.How many would you expect to be male?b.Using the table or tree diagram, construct a contingency table of gender versus age group.c.Using the contingency table, find the probability that out of the age 20–64 group, a randomly selected driver isfemale.113.Approximately 86.5% of Americans commute to work by car, truck, or van. Out of that group, 84.6% drive alone and15.4% drive in a carpool. Approximately 3.9% walk to work and approximately 5.3% take public transportation.a.Construct a table or a tree diagram of the situation. Include a branch for all other modes of transportation to work.b.Assuming that the walkers walk alone, what percent of all commuters travel alone to work?c.Suppose that 1,000 workers are randomly selected. How many would you expect to travel alone to work?d.Suppose that 1,000 workers are randomly selected. How many would you expect to drive in a carpool?114.When the Euro coin was introduced in 2002, two math professors had their statistics students test whether the Belgianone Euro coin was a fair coin. They spun the coin rather than tossing it and found that out of 250 spins, 140 showed a head(eventH) while 110 showed a tail (eventT). On that basis, they claimed that it is not a fair coin.a.Based on the given data, findP(H)andP(T).b.Use a tree to find the probabilities of each possible outcome for the experiment of tossing the coin twice.

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