Question

You own a Roulette Wheel, which has 37 (European Version) equally distributed parts, each has a number number associated. 0 is green, the rest 36 includes 18 red and 18 black. The money you have to pay to the gambler for hitting green, red and black are 10, 1 and 2 dollars respectively. How much you have to charge per play in order to make sure you will make money?

Answer 1

Answer:

To expect a profit in the long run, we have to charge more than $1.73 per play.

Step-by-step explanation:

We hace a roulette wit 37 slots.

One is green, eighteen are red and eighteen are black.

The expected pay for the gambler can be calculated as the sum of the probability of getting green, red or black multiplied by the respective pay.

$E(g)=\sum p_iG_i=p_gG_g+p_rG_r+p_bG_b\\\\\\E(g)=\dfrac{1}{37}(10)+\dfrac{18}{37}(1)+\dfrac{18}{37}(2)\\\\\\E(g)=\dfrac{10+18+36}{37}=\dfrac{64}{37}\approx1.73$

If $1.73 per play is the expected pay that will receive the gambler, we have to charge at least this amount to make sure we will make a profit in the long run.