A telephone survey conducted by the Maritz Marketing Research company found that

Question

A telephone survey conducted by the Maritz Marketing Research company found that 43% of Americans expect to save more money next year than they saved last year. Forty-five percent of those surveyed plan to reduce debt next year. Of those who expect to save more money next year, 81% plan to reduce debt next year. An American is selected randomly.

c. What is the probability that this person expects to save more money next year and does not plan to reduce debt next year?
d. What is the probability that this person does not expect to save more money given that he/she does plan to reduce debt next year?

Explanation / Answer

P(Save more money) = 0.43

P(Reduce debt) = 0.45

P(reduce debt | save more money) = 0.81

So,

P(Reduce debt and save more money)

= P(reduce debt | save more money) * P(Save more money)

=0.81*0.43

= 0.3483

c) P(Save more moneyand doesn't plan to reduce debt)

= P(Save more money) - P(Reduce debt and save more money)

= 0.43 - 0.3483

= 0.0817

d) P(Does not save more money | plan to reduce debt)

= P(Does not save more money and plan to reduce debt) / P(Plan to reduce debt)

= [P(reduce debt) - P(Reduce debt and save more money)] / P(reduce debt)

= [0.45 - 0.3483]/ 0.45

= 0.226

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