## Tuesday, January 08, 2008

### Probability of Bears

There are two bears - white and dark.

1. What is the probability that both bears are male?

If we write m for male and f for female, we have four possibilites: (mf, fm, mm, ff) which means the probability of mm = 1/4 (assuming they are all equally possible).

2. What if I told you one of the bears is male? What is the probability they are both males?

The possible outcomes are (mf, fm, mm), which means the probability they are both males is 1/3.

3. Now, what if I told you that the lighter bear is known to be male. What is the probability they are both males?

1. .5

The gender of the lighter color one would have no relevance of the gender of the darker one in this case.

2. I agree with deekin. the answer to the second question is 1/2, not 1/3.

3. there is definitely a flaw in the reasoning in question #2. Everyone has it right. The chance of both being male if one is known to be male is 50%. So the answer to #3 is also 50%.

4. No, the probability they are both males, given that one of them is male is 1/3. There are still three possibilities (mf, fm, mm), since you don't know which bear is the male one. It's only when you determine that the light one is male, that you get to 1/2.

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