A bet on "black" in Roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin.

a. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.

b. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.

Check the explanation

Step-by-step explanation:

let the money on bet is X.

probability of winning =18/38=9/19

probability of losing =(1-9/19)=10/19

expected outcome =probability *return   =(

Expected value of return after one bet is =(9/19*x)-(10/19*x)=-1x/19

it is negative which is obvious cause casinos are there to earn money.

a) Our best strategy in this case as probability of winning is near by 50 %, we should place a bet of 1 $ each,and when we lose one bet consecutively we should bet twice the amount..

Cause two consecutive losses on black has less probability.

c) In case we have to reach 30 $ we have to use the same strategy as above.

correct answers below:

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204