A marketing firm surveys driving habits; the researcher asks the respondents the

Question

A marketing firm surveys driving habits; the researcher asks the respondents their gender, age group (under 36, 35 Years or older), and whether they prefer driving a car, SUV, or pickup truck. a. Construct a probability model that describes the given situation. b. What is the probability that a randomly selected respondent is male if it is known that they prefer driving a SUV? c. What is the probability that a randomly selected respondent is under 35 if it is known that they are female and prefer driving a pickup truck? As a stockbroker, you recommend two stocks to a client. Each stock has as 60% probability of increasing over the next year. Assuming that the performances of the two stocks are independent of each other. a. What is the probability that both stocks will increase in value over the next year? b. What is the probability that at least one stock will not increase in value?

Explanation / Answer

Answer 6:

Assumptions: all the events are independent; we used Bayes; theorem

Excel formula:

Answer 7:

a) P(both stock increases) = P(stock A increase) * P(stock B increase)

= 0.6*.6 = 0.36

b) P(at least 1 stock not increases) = 1-P(at least 1 stock increases)=1-(.6*.4 + .4*.6 + .6*.6) =0.16

a) prob model tables with marginal & joint probabilities FOR Gender =Male (p=0.5) Age-> <35 35 >35 marginal prob of car likings Car 0.013889 0.013889 0.013889 0.166667 SUV 0.013889 0.013889 0.013889 0.166667 Truck 0.013889 0.013889 0.013889 0.166667 marginal prob of ages 0.166667 0.166667 0.166667 0.5 FOR Gender =Female (p=0.5) Age-> <35 35 >35 marginal prob of car likings Car 0.013889 0.013889 0.013889 0.166667 SUV 0.013889 0.013889 0.013889 0.166667 Truck 0.013889 0.013889 0.013889 0.166667 marginal prob of ages 0.166667 0.166667 0.166667 0.5 b) P(Male |SUV) =P(Male, SUV)/p(SUV) 0.500011 c) P(<35 |Female,Truck)= P(<35,Female,Truck)/P(Female,Truck) 0.083398

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