Outcome payout hhh $10 hht $3 hth $0 htt -$3 ttt $10 thh -$3 tht $0 tth $0 kara is playing a game where she flips a coin 3 times. she wins and loses different amounts of money based on the outcomes. what is the expected value for the game?

Expected value is the sum of the probability of each even times the outcome of the event.

So she wins $10 with probability 2/8, $3 with probability 1/8, $0 with probability 3/8, and loses $3 with probability 2/8.

So,

E = 10(2/8) + 3(1/8) + 0(3/8) - 3(2/8)
=5/4 + 3/8 - 3/4
=7/4

= $1.75

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