The economy for the coming year is expected to be weak with a probability of 0.7. Given that it is weak; you expect a dividend will be declared for stock xyz with a probability of 0.9. However, if the market is not weak next year, then the dividend will be declared with a probability of 0.2.
a) Find the probability that the next year's economy is weak and xyz declares a dividend.
b) Find the probability that a dividend is issued.
c) Find the probability that the next year's economy is weak given that a dividend is issued.