### Expected gain in throwing coins

Question Sample Titled 'Expected gain in throwing coins'

Four fair coins are thrown in a game. If four coins show the same face, $${180}$ will be gained; otherwise,$${20}$ will be gained. Find the expected gain of the game.

A
$${40}$ B $${28.75}$
C
$${62.5}$ D $${22.5}$

 ${P}{(}$Four coins show the same face${)}$ $=\dfrac{{{1}^{{4}}+{1}^{{4}}}}{{2}^{{4}}}$  $=\dfrac{{1}}{{8}}$

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