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December 23rd, 2014, 06:38 AM   #1
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Expected Value

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December 23rd, 2014, 08:14 AM   #2
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Hello, jbergin!

Quote:
An unfair coin shows Heads with probability $\frac{3}{4}$
and Tails with probability $\frac{1}{4}.$
A Head gains \$3 and a Tail loses \$8.
What is the expected worth of a coin flip?

$P(\text{win }\$3) = \frac{3}{4},\;\;P(\text{lose }\$8) = \frac{1}{4}$

$E \;=\;\left(\frac{3}{4}\right)(+3) + \left(\frac{1}{4}\right)(\text{-}8) \;=\;+\frac{1}{4}$


You can expect to win an average of $25\rlap{/}c$ per game.

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