Let P denote probability. Given the following probabilities,
Stock price
The firm is profitable
The firm is not profitable
Low price
Medium price
High price
0.40
0.20
0.10
0.20
0.08
0.02
P(low stock price) = 0.60
P(medium stock price) = 0.28
P(high stock price) = 0.12
P(profitable firm) = 0.70
P(non-profitable firm) = 0.30
By using the Bayes’ theorem, calculate the following probabilities.
(i) P (profitable firm I high stock price), i.e., the probability of the firm being profitable given that the stock price is high
(ii) P (non-profitable firm I low stock price) i.e., the probability of the firm being non-profitable given that the stock price is low