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find the probability that after 10 rounds you have between 93 to 107 dollars.

i am not sure how to start the solution,

thanks,

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- #1

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find the probability that after 10 rounds you have between 93 to 107 dollars.

i am not sure how to start the solution,

thanks,

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HallsofIvy

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Note that the

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Ray Vickson

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It might be a bit easier to simplify the "randomness" as follows: assume that in each play you always start by losing $2; then you gain an additional $0 with probability 0.4 or an additional $3 with probability 0.6. In 10 rounds you will have [itex]D = 100 - 20 + 3S[/itex] dollars, where [itex]S = \sum_{i=1}^{10} X_i,[/itex] and the [itex]X_i[/itex] are iid random variables with distribution P{X=0} = 4/10, P{X=1} = 6/10. What limits on S give D between 93 and 107?

find the probability that after 10 rounds you have between 93 to 107 dollars.

i am not sure how to start the solution,

thanks,

RGV

Last edited:

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Curious3141

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No, I count fewer possibilities that put the expected gain between -7 and +7 inclusive. That's between 1 and 5 losses inclusive, which is 5 possibilities.outsidethat interval since there appear to be fewer of those. The probability you are inside the interval is, of course, 1 minus the probability you are outside.

Note that theorderin which you win or lose is irrelevant.

The complementary set would have 6 possibilities (0 losses and 6 to 10 inclusive). That's more work.

- #5

Curious3141

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First work out how many losses will yield an expected gain between -7 and +7 inclusive. This can be done by solving a simple pair of simultaneous equations (or one equation and one inequality).

find the probability that after 10 rounds you have between 93 to 107 dollars.

i am not sure how to start the solution,

thanks,

Then treat it as a Binomial probability problem and just sum the relevant probabilities.

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so S is a binomal variable with n=10 , p=0.6 and i left to find P([itex]5\leq S \leq 9[/itex]) ?It might be a bit easier to simplify the "randomness" as follows: assume that in each play you always start by losing $2; then you gain an additional $0 with probability 0.4 or an additional $3 with probability 0.6. In 10 rounds you will have [itex]D = 100 - 20 + 3S[/itex] dollars, where [itex]S = \sum_{i=1}^{10} X_i,[/itex] and the [itex]X_i[/itex] are iid random variables with distribution P{X=0} = 4/10, P{X=1} = 6/10. What limits on S give D between 93 and 107?

RGV

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