Bayes Theorem Problems

1. A class consists of 60% men and 40% women. Of the men, 25% are blond, while 45% of the women are blond. If a student is chosen at random and is found to be blond, what is the probability that student is a man?

2. It is known in a certain country that 20% of mothers use spanking as a method of disciplining their children. 85% of the mothers that spank their children use valium, while 25% of mothers that don’t use spanking use valium. Does this data suggest that valium causes mothers to spank their children? Explain.

3. Two different suppliers, A and B, provide a manufacturer with the same part. All supplies of this part are kept in a large bin. in the past, 5% of the parts supplied by A and 9% of the parts supplied by B have been defective. A supplies four times as many parts as B. Suppose you reach into the bin and select a part, and find it is nondefective. What is the probability that it was supplied by A?