We go back in time to visit Rudolph. Things aren't going so well for him. Recall that Rudolph has two girl friends, Pamela and Ruth. Every Saturday night he goes out with one or the other. The probability that he dates Pamela, given that he was out with her the previous Saturday is 0.2, while the probability that he dates Pamela given that he was out with Ruth, the previous Saturday is 0.4. Furthermore, Pamela estimates with probability 0.5 that Rudolph will pop the question, while on a date with her and marry her on the following Saturday. Ruth estimates the proposal with a probability of 0.4. Unfortunately, the wedding caterers are not reliable. If Rudolph marries Pamela there is a 0.3 probability that he will die of food poisoning the following Saturday (a slow acting toxin), while if he marries Ruth that probability increases to 0.5. a) Rudolph is not "absorbed" by marriage. Rudolph's initial probability of dating Pamela is 1.0. How long can Rudolph expect to live? Assume if Rudolph doesn't die the first week, the probability of his dying carries over to subsequent weeks. (i. e he has a 0.3 or 0.5 chance of dying two weeks after marriage)
b) Which caterer is responsible for Rudolph's demise. Is it Pamela's caterer or Ruths? what are probabilities