Consider a game at a carnival where two six-sided dice are rolled, and players wager money trying to predict whether the result is over 7 or under 7:

(a) Suppose the last five totals were 12, 8, 8, 11, 10, and two different players at the carnival react differently to this information: one of them, Brad, says, "this means numbers exceeding 7 are more likely" and bets that the next result will exceed 7. The other player, Chad, says, "actually, a number below 7 is due to happen any moment now!", and bets that the next result will be less than 7. Explain in detail which of them you think is right:

(b) Suppose a player wagers $10 and, if they correctly predict whether the next two dice will sum to a value greater than 7, they earn $8 more (in addition to the $10 they wagered); however, if the dice values are less than 7, they lose their wager and earn nothing. If the dice land on exactly 7, nothing happens, and they get their wager back. Calculate the expected value of playing this game; would you bet money on this game?