In roulette, you may bet whether the number that comes up is odd (or even). (Remember that 0 and 00 do not count as either odd or even and there are numbers 1-36.) The wager pays even money, that is, if you win, you get whatever you bet, and if you lose, you lose that same amount. What is your expected value for this bet

Answer: - 0.027

Step-by-step explanation:

Win = any even number between (0 - 36)

Therefore,

Lose = any odd number between 0 - 36 including 0

Assume Bet amount = $1

Expected value is calculate by summing all possible outcomes by their respective probabilities.

Expected value = [ (p (winning) * net win value) + (p (losing + net loss value]

P (winning) = p (even) = 18/37

P (losing) = p (odd) + p (0) = 19/37

Net win value = $2

Net loss value = $-1

Expected value = [ (18/37) * ($1) + (19/37) * (-$1) ]

Expected value = 0.48648648 - 0.51351351

Expected value = - 0.027