Question

A modified roulette wheel has 44 slots.One slot is 0, another is 00, the others are numbered 1 trough 42 respectively.You are placing a bet that an outcome is an odd number (neither 0 or 00 are even or odd).
a. What is your probability of winning?
b. What are the actual odds against winning?
c. The payoff odds are 1:1. How much profit do you make if you bet $14 and win?
d. How much profit should you make on a $14 bet if the payoff odds are the same as the actual odds against winning?

Answer 1

Answer:

Step-by-step explanation:

There are 44 slots with numbers 0 , 00 , 1 ,2 ...42

Bet is placed for an odd number

Total odd numbers are = 1,3,...41 = 21

Total numbers = 44

a) Probability of winning=n(odd numbers)/total numbers

= $\frac{21}{44} \\=0.4773$

b) Actual odds against winning = $\frac{0.4773}{1-0.4773} \\=0.9131$

c) Pay off odds are 1:1.

So profit if we bet 14 dollars = 14 (0.9131) = 12.7833

d) If pay off is the same as 0.4773:0.5227=0.9131:1

Profit would be =$0.9131*0.9131=\\0.8338$