Two Bears -- A Probability Problem

There are two bears - white and dark.

We may reasonably ask several questions:

1. What is the probability that both bears are male? Writing 'm' for male and 'f' for female and counting the lighter bear first we get four possible outcomes (ff, mf, fm, mm) of which only one should be considered favorable. The answer, therefore, is 1/4.

2. Now assume I told you that one of the bears is male. What is the probability that both are males? Of the three possible outcomes (mf, fm, mm) only the last where both bears are male is favorable. The answer is 1/3.

3. Now the last question. I am telling you that the lighter bear is known to be male. What now is the probability that both of them are males? Please stop for a while and think of the problem. Try to answer the question before looking into the solution.