A modified roulette wheel has 40 slots. One slot is 0, another is 00 and the oth

Question

A modified roulette wheel has 40 slots. One slot is 0, another is 00 and the others are numbered 1 through 38, 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?
(Type an integer or a simplified fraction)

B. What are the actual odds against winning?
The actual odds agasint winning are blank? blank?

C. When you bet that the outcome is an odd number the payoff odds are 1:1 How much profit do you make it you bet $17 and win?

If you win, the payoff is $ blank?

D. How much profit should you make on the $17 bet you could somehow convince the casino to change it's payoff odds so that they are the same as the actual odds against winning?

D.

Explanation / Answer

Solution:

a) The probability of winning(odd or Even) is,
P(Odd) = 19/40 = 0.475
Hence, the required probability is, 0.475

b) The actual odds against winning is,

P(Even)/P(odd) = (40-19/40)/(19/40) = (21/40)/(19/40)
= 21/19
= 21:19

c) If you win, the payoff is, $17
The payoff adds against event A represnt the ratio of net profit to the amount bet.
Payoff odds against A = (net profit):(Amount bet) = 1:1
If the payoff odds are a:b and the bet is c, the payoff is (a*c)/b = (1*17)/1

d) The actual odds against winning are 21:19
(a*c)/b = 21*17/19
= 357/19
= 18.7894
= $18.79

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