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Posted by Paul Hollander on October 25, 2001 at 19:20:00:
In Reply to: Hmmm... posted by YSA on October 24, 2001 at 22:21:49:
:
: Let me take your logic and apply it to a coin toss...
: If I toss a coin, I have a 1/2 (0.50) likelihood of getting heads, and a 1/2 (0.50) likelihood of getting tails.
: Applying your logic to 4 coin tosses, my likelihood of getting 4 heads is 1/2 * 1/2 * 1/2 * 1/2 = 0.0625. Again, applying your logic, my likelihood of getting AT LEAST 1 tail is therefore 1 - 0.0625 = 0.9375.
: Let's take this a little further and apply your logic to 50 coin tosses. In this case, my likelihood of getting all heads is 8.881784e^-16, and my likelihood of getting AT LEAST 1 tail is 1 - 8.881784e^-16 = 0.9999.
: So...using your logic, I could toss a coin 50 times and yet still only be 99.99% sure of getting AT LEAST 1 tail.
: It seems to me that your logic only leaves 2 possibilities for me to be 100% certain of getting AT LEAST 1 tail from tossing a coin:
: - Toss the coin an infinite number of times
: - Use a 2-tailed coin
You got it.
: I don't know about you, but my money is on tails showing up AT LEAST once during 50 coin tosses.
With odds of 99+%, mine would be, too. That doesn't mean I'd win all the time, just most of the time.
: Getting back to ball pythons, the same applies...
: The only way to achieve 100% likelihood of producing an albino (according to your logic) would be to produce an infinite number of eggs from an infinite number of breedings. (Hmmm...I'd always assumed that all those hets that didn't produce had been sold by scam artists...perhaps they had been studying your logic).
: Anyway, since you have not pointed out any flaws in my previous posts, I still believe that my logic more accurately represents what should be expected from 4 eggs produced from a het to het breeding. ie: Likelihood of 1 albino from 1 egg = 25%. Likelihood of AT LEAST 1 albino from 4 eggs = 4 * 25 = 100%.
By this logic, the likelihood of AT LEAST one normal from a four egg clutch is 4 * 25% = 100%. And the likelihood of AT LEAST one heterozygote is 4 * 50% = 200%. (How can you have a 200% probability of something happening?) If you have three albinos in the clutch then the clutch lacks either a heterozygote or a normal. Which, by your logic, is impossible.
: Consider what my figures mean, however...
: My figures are 'statistics'; this means that my figures will tend to hold true the closer we get to having an infinite number of eggs. So, as we get closer to an infinite number of eggs, your logic implies a 100% likelihood of producing AT LEAST 1 albino, and so does mine. The major difference, however, is that my logic addresses the frequency at which I would expect this to occur...1 out of every 4 eggs.
Your fallacy is that you are expecting at least one albino in EVERY four egg clutch. Now if you were expecting around 2500 albinos from 10000 eggs, I'd agree with you.
Using your coin tossing analogy, the odds of getting heads in any given toss is 50%. By your logic, the odds of getting at least one heads in two tosses are 2 * 50% = 100%. I just did a series of five two-coin tosses. One was two tails, and the rest were one heads and one tails. Seems like the real world doesn't agree with your logic.
Paul Hollander
