牧龙在野!

Prospect theory is a theory that describes decisions between alternatives that involve risk, i.e. alternatives with uncertain outcomes, where the probabilities are known. The model is descriptive: it tries to model real-life choices, rather than optimal decisions.

这个理论很有趣的一点是：人们对金钱上的收入和损失的心里感受是完全不平均的。当你得到一点点的时候，你满足感会上升的很快，以至于你持续得到很多钱以后，你的满足感反而上升的变慢了；当你失去一点钱的时候，你很痛苦，但是随着你失去的越来越多，你反而不会像以前那么痛苦了。

                                      

In probability theory, Bayes' theorem (often called Bayes' Law) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)

As a formal theorem, Bayes' theorem is valid in all interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates at greater length.

A woman applies for two jobs, job A and job B. She thinks that she has 60% chance of getting job A and a 50% chance of getting job B. She also thinks that if she gets A, then the chance of her getting B increases to 70%.

Required:
1. Find the probability that she will get one job exactly;
2. Find the probability that she will get both jobs.
3. Find the probability that she will get job A if she knows already that she has get job B.