Re: Looking for probability problems.

Androcles wrote:
"Greg Hansen" <glhansen@xxxxxxx> wrote in message news:erdk1302dgq@xxxxxxxxxxxxxxxxxxxxx
I'm looking for a collection of problems and solutions in probability and related set theory. I'm not looking for a text book or review book, really. Just practice. Any suggestions?


Here is a set of 6 fair dice:
Die 1 has faces numbered 1,7,7,7,7,7
Die 2 has faces numbered 2,2,8,8,8,8
Die 3 has faces numbered 3,3,3,9,9,9
Die 4 has faces numbered 4,4,4,4,10,10
Die 5 has faces numbered 5,5,5,5,5,11
Die 6 has faces numbered 6,6,6,6,6,6


Player A selects a die and throws it. Player B selects a die from those remaining and throws.
The winner is awarded the difference between the outcomes.
When player A selects a die and throw it, what is the probability that B
will throw a higher number than A when B throws his selection from those remaining,
a) if B selects his die at random?
b) if B does not know what the outcome of A's throw was?
c) if B knows what the outcome of A's die was?

Solutions:
a) is a zero sum game.
b) 5/6
c) knowledge is power. If A has 11 showing, B must minimize his loss.
If A has 1 showing, B must maximize his gain.
What should B choose?




Cute. The means are all the same, but the mean differences are not zero.
.

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