Question 1127159
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Let x be the probability of winning; then 1-x is the probability of losing.<br>
The game is fair if the expected value is 0.<br>
To find the expected value, find the product of each outcome and its probability and add the products.<br>
There are two possible outcomes: win (value +7, probability x) or lose (value -3, probability (1-x))<br>
{{{(+7)(x)+(-3)(1-x) = 0}}}
{{{7x-3+3x = 0}}}
{{{10x = 3}}}
{{{x = .3}}}<br>
The probability of winning is 0.3, or 30%.