whats the average score of choosing a random num 1-100?

[Shroomy]

Can anyone help me out here.
I know I used to know how to compute this .. but I must have killed off those brain cells at some point.

Say a person picks a random number between 1 and 100 and his score is the highest number he picks.

What is the average score going to be for 2 choices.
How about N choices?

for example I had a bowl of chips with the numbers 1-100 written on them, and I picked out 5 of them. What would I expect my average score (highest number) to be for my 5 choices if I repeated this "many" times?

Thx [img]/images/graemlins/smile.gif[/img]


P.S. You get extra credit and a star sticker if you can figure out what this has to do with my other post about hand ranges. [img]/images/graemlins/cool.gif[/img]

[BruceZ]

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Say a person picks a random number between 1 and 100 and his score is the highest number he picks.

What is the average score going to be for 2 choices.

[/ QUOTE ]

Assuming that you are drawing with replacement (so that you can pick the same number more than once) this is the same as the problem I solved in this post. That was for 5 choices, so the formula for 2 choices is

100 - (1^2 + 2^2 + 3^2 + ... 99^2)/100^2 = 67.165.

You can do this in Excel, or you can use the formula for this power sum.


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How about N choices?

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100 - (1^N + 2^N + 3^N + ... + 99^N)/100^N


[ QUOTE ]
for example I had a bowl of chips with the numbers 1-100 written on them, and I picked out 5 of them. What would I expect my average score (highest number) to be for my 5 choices if I repeated this "many" times?

[/ QUOTE ]

Again assuming that you put back the chip each time, or that you have an extremely large bowl with each number represented many times, the average highest number is about 83.8.