5.4 solutions

# 1 speeding ticket got 0 or 1 speeding tickets has a

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>1 speeding ticket Got 0 or 1 speeding tickets Has a fast car .12 .03 Doesn’t have a fast car .19 .66 P(fast| less than 1 ticket) = = .387 P(fast) = .15 These probabilities are not equal, so owing a fast and getting less than 1 speeding ticket are NOT independent. Problem 4 Exactly three restaurants serve a small town in Ohio. Restaurant A has 50% of all the business, restaurant B has 30% and restaurant C has the rest of them (20%). Customer satisfaction rates are 80%, 65%, and 40%, respectively. a. Make a tree diagram and a table from the probabilities above. Include clear labels for all probabilities and events. .6 .4 .35 .65 .2 .8 .5 .3 .2 S NS A .4 .1 .5 B .195 .105 .3 C .080 .120 .2 .675 .325 1.0 A B C S A NS A S B NS B S C NS C

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b. You are going to eat at a restaurant in this small town in Ohio (so it has to be one of these 3 restaurants). Based on the information given, what is the chance that you will be satisfied? P(S) = (.8)(.5) + (.65)(.3) + (.4)(.2) = .675 (the sum of column 1 in the table) c. Suppose you ate at one of these restaurants and you were not satisfied. What is the chance you ate at Restaurant C? Use probabilities and show your work. P(C NS) = P(C)P(NS C ) P(NS) = (. 2 )(. 6 ) . 325 = . 369 Problem 5 Given the following information, compute all four ‘and’ probabilities and enter them into the correct places in the table below. (Remember, your joint probabilities should all sum to one.)
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