Bayesian revision of probabilities
The manager of ABC Co. is concerned that a competing firm might be planning to introduce a new product that could seriously affect his sales. He feels that the chances are only one in five that the competitor is actually planning to introduce a new product.
He then discovers that the competitor is building a new plant. After careful consideration he decides that if a new product is to be introduced the odds would be 3 to 2 in favour of the building of a new plant, but if a new product is not to be introduced, the odds would be 4 to 1 against the building of a new plant.
(a) What is the manager's prior probability that his competitor is planning to introduce a new product?
(b) What is his revised probability of a new product given that the competitor is building a new plant?