Suppose you wanted to guarantee that you would win on at least one number for on

Question

Suppose you wanted to guarantee that you would win on at least one number for one roulette wheel spin. Imagine betting a dollar on every red and every black number (1 through 36), and also on the green o. In order to place all of your bets, how much would you have to spend? $ 37 (a) (b) Since you bet on all the possible outcomes, you are guaranteed to win a single bet. What is the total paid back to you (that includes any winning bet amount that you got back)? 36 (c) How much is your total profit/loss? (Hint: Profit = Revenue-Expenses)? $ -1 (d) Another way of thinking about this betting scenario is in terms of profits or losses per bet. You made 37 bets. What is the single bet that won? $ 36 What is the profit for each of the 36 bets that lost? $ -36 Write an equation that shows how to compute the total profit. (Hint: You should get the same answer as in part (c).)

Explanation / Answer

(d)

Profit for single bet that won = Revenue - Expense = $36 - $1 (We spent $1 on the single bet which won $36)

= $35

So, answer is 35

Profit for each of the 36 bets that lost = Revenue - Expense = $0 - $1 (We spent $1 on each of the single lost bet which gave us nothing)

= -$1   

So, answer is -1

Total Profit = Sum of profits of 1 won and 36 lost bets

= 1 * $35 + 36 * (-$1)

= $35 - $36

= -$1

This is the same answer as in part (c).

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