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 $14

Explanation:

Step1: Understand the pay - off odds formula

The pay - off odds formula is \( \text{Pay - off odds}=\frac{\text{Net profit}}{\text{Amount bet}} \). Given pay - off odds \( = 1:1\), which means for every dollar bet, the net profit is \(1\) dollar.

Step2: Calculate the profit

We use the formula \( \text{Net profit}=\text{Pay - off odds}\times\text{Amount bet} \). Substitute the amount bet \(=\$18\) and pay - off odds \( = 1\) (since \(1:1\) implies a multiplier of \(1\)) into the formula.

Answer:

The profit is \(\$18\)