Question 1099170
<br>What does "lands with a tail on top during the three tosses" mean?<br>
It sounds as if it means tails at least once on the three tosses.  If that is the case, I want to know where I can play this game, because I'm going to win 7 out of 8 times.  The only way not to win is to get heads on all three tosses; the probability of that is (1/2)(1/2)(1/2) = 1/8; so the probability of winning is 7/8.<br>
If that is indeed the rule, then when you play the game 8 times you pay $2 each time (-$16); you win 7 times (+$70), and you lose 1 time (no change).  So for each 8 games your expected net would be +$54.  So the expected value of each game is $54/8 = $6.75.<br>
I don't think it is likely that that is the way the problem is supposed to go.  I suspect the rule is you win if you get tails on ALL THREE tosses.  Then the probability of winning is 1/8 and the probability of losing is 7/8.<br>
Then for 8 games you would again be paying $16, but you would only be winning $10 once.  So you would lose $6 every 8 games; that means the expected value for each game would be -$6/8 = -$0.75.