一道概率论的题

Suppose that when a machine is adjusted properly, 50% of the items produced by it are of high quality and the other 50% are of medium quality. Suppose, however, that the machine is improperly adjusted during 10% of the time and that, under these conditions, 25% of the items produced by if are of high quality and 75% are of medium quality.
Suppose that five items produced by the machine at a certain time are selected at random and inspected. If four of these items are of high quality and one item is of medium quality. What's the probability that the machine was adjusted properly at that time?
Suppose that one addional item,which was produced by the machine at the same time as the other five items,is selected and found to be of medium quality.What is the new posterior probability that the machine was adjusted properly
当一个机器正常运转，50%几率生产高质量产品，50%生产中等质量产品。然而该机器在10%的时间运转不正常，在这些条件下产生的产品，25%是高质量的，75%是中等质量。
假设五个项目在某一个时间机器生产的选择在随机和检查。如果这四个项目都是高质量的，一项是中等质量。那机器是当时正常工作的概率？
假设一个额外的项目，这是在为其他五个项目同时由机器产生的，是选择和发现是中等质量。该机进行适当调整新的后验概率是什么？

首先，写的第一场比赛，还没有使用新球在框中分布规律;
联合概率分布规律的经典获得了两项新的球被取出的情况下，各种不同的值;
>最后一页的各种情况下的概率（该产品的两个概率）叠加。

f(x)、g(x)、h(x)分别在负无穷到正无穷上积分得1 af(x)+bg(x)+ch(x）在负无穷上到正无穷上积分也必须得1 由积分的性质可知 af(x)+bg(x)+ch(x）在负无穷上到正无穷上积分=a+b+c=1 因为是概率密度函数，概率密度函数在其整个积分域上的积分是得1的。 概率密度函数积分是分布函数，整个积分域积分就相当于分布函数在整个域上的概率，因此必须为1.