Question 1131743
<br>
P(spade) = 1/4; P(not spade) = 3/4.<br>
Value (spade) = $10 (-$5 for playing, +$15 for winning)
Value (not spade) = -$5<br>
Expected value of playing: {{{(1/4)(10)+(3/4)(-5) = 10/4-15/4 = -5/4}}}<br>
The expected value of playing the game is -$1.25.<br>
To make the game fair (make the expected value of playing equal to 0), the cost for playing the game should be x, where<br>
{{{(1/4)(15-x)+(3/4)(-x) = 0}}}
{{{15/4-(1/4)x - (3/4)x = 0}}}
{{{15/4-x = 0}}}
{{{x = 15/4 = 3.75}}}<br>
ANSWER: The price for playing the game, to make the game fair, should be $3.75.