There are "3+6=9" balls in a box. Winner takes two balls at random without replacement.
Let "X=" gain.
"P(WB)={3 \\over 9}\\cdot{6 \\over 8}={1 \\over 4},\\ \\ \\ X=15-5=10"
"P(BW)={6 \\over 9}\\cdot{3 \\over 8}={1 \\over 4},\\ \\ \\ X=-5+15=10"
"P(BB)={6 \\over 9}\\cdot{5 \\over 8}={5 \\over 12},\\ \\ \\ X=-5-5=-10"
Find his expected gain
"{1 \\over 12}(30)+{1 \\over 4}(10)+{1 \\over 4}(10)+{5 \\over 12}(-10)={10 \\over 3}"
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