The document discusses the probability of a company having a good year and issuing a dividend. There is a 65% chance the coming year will be good. If the year is good, the chance of a dividend is 80%. If the year is not good, the chance of a dividend is 15%. To calculate the probability the year is good given a dividend is issued, the document uses Bayes' theorem and determines the chance is 90.83%.
The coming year is expected to be a good one for your company with p.pdf
1. The coming year is expected to be a good one for your company with probability 0.65. Given
that it is a good year, you expect that a dividend will be declared with probability 0.80. However,
if it is not a good year, then a dividend will occur with probability 0.15
Question: If dividend is issued, what is the probability that it is a good year?
Solution
P(good year | dividened) =
P(good year and dividened | dividened) =
P(dividened | good year)*p(good year) / (P(dividened | good year)*p(good year) + P(dividened |
not good year)*p(not good year)) =
(0.8*0.65)/(0.8*0.65 + 0.15 * 0.35) = 0.9083
