John is the marketing advisor for the business that is considering whether or no

Question

John is the marketing advisor for the business that is considering whether or not to design a new chair. Assuming the market for the chair will either be weak or it will be strong. John has estimated there is 55% possibility that the market for the chair will be strong.

Before making the decision to produce the chair, John embarks on a statewide survey. The survey results are inaccurate. Prior results show that if the market is not strong, there is a 15% chance that the survey result will be positive. But, a market that is strong, will have a 10% chance that the survey result will be negative.

Find the following two probabilities:

The probability that the market for the chair will be strong given the positive survey result;

The probability that the market for the chair will be strong given the negative survey result.

Explanation / Answer

1)P(positive survey result)=P(strong market and positive survey result)+P(weak market and positive survey result) =0.55*(1-0.1)+(1-0.55)*0.15=0.5625

hence P(strong market|positive survey result)

P(strong market and positive survey result)/P(positive survey result)

=0.55*(1-0.1)/0.5625=0.88

2)

P(negaive survey result) =1-P(positive survey result)=1-0.5625=0.4375

P(strong market|positive survey result)

=P(strong market and negative survey result)/P(negative survey result)

=0.55*0.1/0.4375=0.125714

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