onsider a marriage market where men come in two types: cads and lads. Lads are 60% of the population while Cads make up the remaining 40%. Both types can act either nice or mean and the probabilities of such behavior are P(Nice|Lad) = 0.6; P(Mean|Lad) = 0.4; P(Nice|Cad) = 0.4; P(Mean|cad) = 0.6. A woman goes on a first date with a man, trying to figure out his type, and the man acts Nice.

a) What was her estimate of the probability that he was a Lad before the first date (prior) and after the first date (posterior)?

b) It turns out that the marginal cost of intensive search will outweigh the marginal benefits when the woman's estimated probability of having a Lad reaches 0.960. Given the probabilities from above, what is the least number of dates the couples will have to have before she becomes willing to tie the knot?