Question

Suppose we draw two cards out of a deck of 52 cards. If the two cards make a pair of “face” cards (jacks, queens, or kings), you collect $200; if they makes a pair of aces, you collect an amazing $1,000; if they make a pair but not a pair of face cards or aces, you collect $100; otherwise you lose $13. In terms of profits and statistics, should you play the game? Why or why not?

Answer 1

let X is profit made by you on this bet)

P(X=200) =P(pair of face cards) =3*(4*3/(52*51))=0.013575

P(X=1000) =P(Pair of ace )=4*3/(52*51)=0.004525

P(X=100) =P(pair other than ace and face cards) =9*(4*3/(52*51))=0.040724

P(X=-13) =P(cards other than pair) =1-13*(4*3/(52*51))=0.941176

therefore expected value of the game =E(X)=xP(x)

=200*0.013575+1000*0.004525+100*0.040724+(-13)*0.941176= $ -0.92

since expected value from playing this game is negative one should not play this game