Question

There is a game at the local carnival where you pay $1 for a chance to draw one card from a standard deck. If you draw an ace, you win $3.50 and if you draw a face card, you win $2. Otherwise you don’t win anything. Find the expected value to you for this game. Explain why it is or is not a good idea to play this game.

Answer 1

Price of game = $1          
There are 4 aces and 12 face cards in a deck of 52          
P(drawing an ace) = 4/52          
P(drawing a face card) = 12/52          
P(drawing any other card) = (52-4-12)/52 = 36/52          

Expected Value for the game = $0.26923 + $0.46154 + 0          
       = $0.73077  
Expected Value for the game = rounding to 2 decimals     
          
          
Expected Value for the game is $ 0.73 which is less than the price $1 that we pay for the draw          
Thus, there is higher probability of making a loss          
Hence, it is not a good idea to play this game          

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