I think the larger effect is treating the probabilities as independent when they’re not.
Suppose I have a jar of jelly beans, which are either all red, all green or all blue. You want to know what the probability of drawing 100 blue jelly beans is. Is it 13100≈2⋅10−48? No, of course not. That’s what you get if you multiply 1⁄3 by itself 100 times. But you should condition on your results as you go. P(jelly1 = blue)⋅P(jelly2=blue|jelly1=blue)⋅P(jelly3=blue|jelly1=blue,jelly2=blue) …
Every factor but the first is 1, so the probability is 13.
I think the larger effect is treating the probabilities as independent when they’re not.
Suppose I have a jar of jelly beans, which are either all red, all green or all blue. You want to know what the probability of drawing 100 blue jelly beans is. Is it 13100≈2⋅10−48? No, of course not. That’s what you get if you multiply 1⁄3 by itself 100 times. But you should condition on your results as you go. P(jelly1 = blue)⋅P(jelly2=blue|jelly1=blue)⋅P(jelly3=blue|jelly1=blue,jelly2=blue) …
Every factor but the first is 1, so the probability is 13.