Question 1110509
E(X)=(1/4)*10-(3/4)*4=$2.50-$3.00=-$0.50.
BUT
he pays to play the game, so if he wins, he gets $10 minus $4 or $6.
E(X)=(1/4)*6-(3/4)*4=$1.50-$3.00=-$1.50 

It needs to be clear whether he gets back the money he paid to play.  I suspect he doesn't, so the expected value is -$1.50.