I am sitting here trying to set up a 2 x 2 table and keep coming up with funky results. The question is: Suppose that 30% of the population have characteristic A and 40% have charactersitic B. Assume that the probabilities are independent.

What is the probability that a person selected at random from this populateion will have both characteristics. I take this to be the union of

of A and B and believe that the answer is .3 + .4 = .7. This is clearly not correct. It is way to high.

What is the probability of having Characeristic A among people who have charteristice B?

What is the probability of haing Chaacteristic A among peope who do not have characteristic B?