Question

A market research company conducts surveys to forecast short-run economic outlook. Based on past performance, 94% of its surveys that forecasted economic conditions as “Favorable” were correct (that is, P(Survey result is Favorable | Economy is Favorable) = 0.94), while 90% of its surveys that forecasted economic conditions as “Unfavorable” were correct. If a pre-survey, subjective probability for “Favorable” economy is 0.65, what is the probability that the economy is “Favorable” if the company's survey forecasts “Favorable” economy?

0.611

0.646

0.946

1.000

Answer 1

P(Survey result is Favorable | Economy is Favorable) = 0.94

P(Survey result is not Favorable | Economy is not Favorable) = 0.90

P(Survey result is Favorable | Economy is not Favorable) =1- 0.90 = 0.1

P(Economy is Favorable) = 0.65

P(Economy is not Favorable) = 1- 0.65 = 0.35

P(Economy is Favorable | Survey result is Favorable) =

P(Survey result is Favorable | Economy is Favorable) * P(Economy is Favorable) /   P(Survey result is Favorable | Economy is Favorable) * P(Economy is Favorable) + P(Survey result is Favorable | Economy is not Favorable) *

P(Economy is not Favorable)

= 0.94 * 0.65 / (0.94 * 0.65) + (0.1 *0.35)

=0.611/ .646

= 0.946

Please revert back in case of any doubt.

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