In the first eKnow example in which we used binomial probabilities, suppose the results had been that 4 out of the 20 people responded that they would purchase the eKnow. Use Bayes’ theorem to find your posterior probability P (Hit | r = 4; n = 20) for the following pairs of prior probabilities:
a. P (Hit) = 0.2; P (Flop) = 0.8
b. P (Hit) = 0.4; P (Flop) = 0.6
c. P (Hit) = 0.5; P (Flop) = 0.5
d. P (Hit) = 0.75; P (Flop) = 0.25
e. P (Hit) = 0.90; P (Flop) = 0.10
f. P (Hit) = 1.0; P (Flop) = 0
Create a graph of the posterior probability as a function of the prior probability.