Kittens - a start!

Well, I hope one or two of you are enjoying thinking about kittens and probabilities! It's almost time for me to head on vacation, with little time to finish posting (I'll be back in a week and a half). Let me start with the answer to questions 1a and 1b: the probabilities that one kitten is male, the others female, or vice versa. See if that starts any further thinking on the other questions.

One important hint: think binomial distribution. Now it's not as nasty as it looks on the link.

Without all the math, look at it this way: suppose we're just adding random kittens to a litter. A binomial distribution happens when you have a 50% probability of an event (in this case, say, adding a male kitten to a litter) - and that event has the some number of opportunities to happen. The probability of of having n males after I add a new kitten is logically the sum of probabilities that:

we had n-1 males in the litter before adding the new kitten, and now I added a male (50%), plus

we had n males, and I added a female (also 50%).

So basically, you start out with 1 kitten : its 50/50 that it's male, right? With two kittens, you have 25% chance of no males (because you couldn't have n-1 to apply the first bullet item, right? All that's left is the original 50% chance we started a female, times a 50% chance I don't pick a male this time); then 50% chance of one male (apply both bullet items); 25% chance of two (because for two you can't apply the second bullet item). The totals, predictably, add up to 100%

So for three kittens (our case), you take that distribution to the next step. From the chart below, the chance of only one male is 3 out of 8 - 3/8. The chance of two males: also 3/8. The answer to 1a is 3/8. And the answer to 1b is 3/8 + 3/8, or 3/4.

There's some cool math behind it when you get into the details, but I'd better stop there!

See y'all late August, ok?

Table showing probability of n males in a total population. Divide the numers under the columns by the "total chances".

population	0	1	2	3	4	5	Total chances
1	1	1					2
2	1	2	1				4
3	1	3	3	1			8
4	1	4	6	4	1		16
5	1	5	10	10	5	1	32