Question

a modified roulette wheel has 28 slots. one slot is 0, another is 00, and the others are numbered 1 through 26, respectively. you are placing a bet that the outcome is an even number. (in roulette, 0 and 00 are neither odd nor even.)
a. what is your probability of winning?
the probability of winning is \\( \frac { 13 } { 28 } \\)
(type an integer or a simplified fraction.)
b. what are the actual odds against winning?
the actual odds against winning are 15:13.
c. when you bet that the outcome is an even number, the payoff odds are 1:1. how much profit do you make if you bet $18 and win?
if you win, the payoff is $ 18.
d. how much profit should you make on the $18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning?
$ (round to the nearest cent as needed.)

Explanation:

Step1: Recall the formula for profit from pay - off odds

The formula for profit when the pay - off odds are \(a:b\) and the bet amount is \(B\) is \(Profit=\frac{a}{b}\times B\).

Step2: Identify the values of \(a\), \(b\), and \(B\)

From part (b), the actual odds against winning are \(15:13\), so \(a = 15\), \(b=13\), and the bet amount \(B = 18\).

Step3: Calculate the profit

Substitute the values into the formula: \(Profit=\frac{15}{13}\times18=\frac{270}{13}\approx20.77\)

Answer:

\(20.77\)