SOLUTION: suppose you play a single number in a roulette 100 times. use the poisson model to estimate th eprobability of winning five or more times.
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Question 612450: suppose you play a single number in a roulette 100 times. use the poisson model to estimate th eprobability of winning five or more times.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Poisson is utterly inappropriate for this question. You want the binomial distribution.
Also, you don't mention whether you are playing with an American or a European wheel.
I'll assume an American wheel and you can adjust the probability of individual success if you want a European wheel. The probability of 5 or more is a very long and complex calculation requiring you to calculate the sum of the probability of exactly 5 plus exactly 6, and so on up through exactly 100 (a very tiny number indeed), but the probability of 5 or more is equal to 1 minus the probability of 4 or less, a much simpler calculation.
\ =\ 1\ -\ P_{100}\left(\leq{4},\frac{1}{38}\right)\ =\ 1\ -\ \sum_{i=0}^4\,{{100}\choose{i}}\left(\frac{1}{38}\right)^i\left(\frac{37}{38}\right)^{100\,-\,i})
You can do your own arithmetic.
Hint: 
is the number of combinations of 
things taken 
at a time and is calculated by !})
John
My calculator said it, I believe it, that settles it
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