A card is drawn at random from a deck of playing cards. If it is red, the player wins 1 dollar; if it is black, the player loses 2 dollars. Find the expected value of the game.
I think that the number of cards in the deck may have something to do with it, and the decreasing number of red cards and black cards affect the probability of the draw being black or red which in turn affect the expected value of the game. For the most part I have no idea how this is supposed to work, I have made no successful or failed attempts to solve this question because I have no knowledge to go on.
Best Answer
The expected value of the game is $$ \sum_{a_i}a_ip(a_i), $$ where $a_i$ is a possible payout of the game and $p(a_i)$ is the probability of that payout occuring. Applying this to your problem gives $$ E[X]=1\times1/2+(-2)\times 1/2=-1/2 $$