Well For the first one there is no formula I'm using just my common sense.

Is there another way to think about this problem or maybe there is a formula I'm missing here?

I multiplied because i know that or is logical +, and is logical multiplication. But guess that is not the case here.

So if an object was detected, *and *it was the second locator that did it is A and B.

By your explanations i should just have a solution with P(A|B) = 0.90 / 0.87 ?

No, this would be an impossible probability, since it is greater than 1.

I guess what I'm really hoping for from you is an indication of what you have

*learned *about probability. There

*is *a formula for the first question: P(A) = P(A|B

_{1})*P(B

_{1}) + ... + P(A|B

_{n})*P(B

_{n}) , where B

_{1} through B

_{n} are mutually exclusive events that together cover the entire sample space (a partition). In your case, they are "first locator is chosen, second locator is chosen, ...", and the probability of each of them is 1/4; so the formula amounts to [P(A|B

_{1}) + ... + P(A|B

_{n})]*(1/4), which is your average. Have you learned anything of the sort, that you would be expected to use for this problem?

"Or" being addition and "and" being multiplication is a general statement that has to be made precise; Each has a general form (more complex) and a special case (mutually exclusive and independent, respectively) in which it is as simple as it can be. Surely you have learned these fuller forms.

This is a good place to see what I am referring to.

Here is one site that includes these and many other rules, including the "law of total probability", listed under Bayes' Rule, which is what I mentioned for the first part. The general cases are stated succinctly

here.