SOLUTION: the cost to play a card game is $10. You pick a card from a deck of cards and if you get a jack you win $10, if you pick a red king you win $25. what is the expectation of this g

Question 1041741: the cost to play a card game is $10. You pick a card from a deck of cards and if you get a jack you win $10, if you pick a red king you win $25. what is the expectation of this game?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let X = the r.v. denoting the net earning after a single draw.
The probability of getting a jack is 4/52 = 1/13. The net earning after picking a jack is $10 - $10 = $0.
The probability of getting a red king is 2/52 = 1/26. The net earning after picking a red king jack is $25 - $10 = $15.
The probability of neither getting a jack nor a red king is 46/52 = 23/26. The net earning after picking is $0 - $10 = -$10.
===> E(X) = 0*(1/13) + 15*(1/26) + (-10)*(23/26) = -$8.27. (Which is a loss!)
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