A game is being played using one die. If the die is rolled and shows 4, the player wins $25. If the die shows any number other than 4 the player wins nothing. If there is a charge of $5 to play game what is the expected value?

Question

anonymous · Answer

it is the amount you win times the probability you win it

anonymous · Answer

you win with probability $\frac{1}{6}$ and lose with probability $\frac{5}{6}$  it is 
$$20\times \frac{1}{6}-5\times \frac{5}{6}$$ the reason for $20$ instead of $25$ is that even if you win, you already payed $5 to play