Question

# A modified roulette wheel has 28 slots. One slot is​ 0, another is​ 00, and the...

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.)

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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