Can you?
| | Did you see that lovely Planet Earth Polar bear thing? Well consider this: 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.
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Male bears, first solution to the last question
Since it's now given that the lighter bear is male there are only two possible outcomes (mf, mm). Thus the probability that both are male goes up to 1/2. Note how each additional piece of information changed the number of possibilities and, hence, the probability of the outcome.
Male bears, second solution to the last questionThe sequence of three question is supposed to lead one on to wondering what difference does it make to specify that the white bear is male. And, in my experience, the trick works too. But since it's now known that the white bear is male, its sex is removed from the realm of random. All that matters is the sex of the dark bear who is believed to be male with the probability of 1/2. A short way to express the same idea is as follows:
P("both are male" | "white is male" ) = P("dark is male" )
where P(A|B) means the (conditional) probability of A provided B is known to take place.
SM
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Andrew (22.11.06 17:24) nearly understood that one |
