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

eveneven

number. (In roulette, 0 and 00 are neither odd nor even.)

a. What is your probability of winning?

The probability of winning is

nothing.

(Type an integer or a simplified fraction.)

b. What are the actual odds against winning?

The actual odds against winning are

nothing:nothing.

c. When you bet that the outcome is an

eveneven

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

$nothing.

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?

$nothing

(Round to the nearest cent as needed.)

Answer #1

a) As 0 and 00 are neither odd nor even and the rest 26 slots
have numbers from 1 to 26. Therefore the probability of winning is
computed here as:

= P(Even number)

= 13/28

**therefore 13/28 is the required probability
here.**

b) The actual odds against winning is computed here as:

= Number of outcomes of losing / Number of outcomes of winning

= 15 / 13

**therefore 15:13 are the required odds here.**

c) Given the payoff odds is 1:1, the profit made when we win is
the same as the betting amount computed as $18. **Therefore
the total payoff here is $18.**

d) In case the odds are changed to the actual probability odds, the amount won is computed in that case is:

= Odds of winning * Bet amount

= (15/13)*18

= $20.77

**Therefore $20.77 is the profit amount in that
case.**

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