# Posterior probability

Using the following information about the accuracy of a market research firm:

Probability of a favorable study given a favorable market = 0.7

Probability of an unfavorable study given a favorable market = 0.3

Probability of a favorable study given an unfavorable market = 0.05

Probability of an unfavorable study given an unfavorable market = 0.95

If there is a 0.60 prior probability of a favorable market, find the following possibilities:

a. the probability of a favorable market given a favorable study.

b. the probability of an unfavorable market given an unfavorable study.

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#### Solution Preview

Using the following information about the accuracy of a market research firm:

Probability of a favorable study given a favorable market = 0.7

Probability of an unfavorable study given a favorable market = 0.3

Probability of a favorable study given an unfavorable market = 0.05

Probability of an unfavorable study given an unfavorable market = 0.95

If there is a 0.60 prior probability of a favorable market, find the following possibilities:

Prior probability of a favorable market= 0.6 (given)

Therefore prior probability of an unfavorable market= 0.4 = 1 - 0.6

( As probability of favorable market + probability of unfavorable market = 1)

This is because there are only two possibilities - favorable and unfavorable market and one of them must exist

Probability of ( A & B happening together) = Probability of A x Probability of B given A

a. the probability of a favorable ...

#### Solution Summary

The solution calculates posterior probability