A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has 38 slots: 18 are black, 18 are red, and 2 are green). A) Try to calculate required number of spin for average(μ) loss corresponds to the certain amount of his initial money (M) completely. Around this average loss, what is the confidence interval (95% or μ±2σ ) of the money (the variance (σ2 ) of the process should be calculated as well)?b)RV x is money (won (n times) or lost(N-n times) amount where N is number of spin, e. G. 25, 50, 100, 200, 400, 500,. 1500…) try to establish a distribution and all moments of this RV. Try to explain whether his decision is sustainable or not. Try to find a winning strategy. Plot the probability density function for various N values.

Question

28-01-2025
Mathematics

High School

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A gambler plays roulette game and he is insisting to play all his money to black (A roulette wheel has 38 slots: 18 are black, 18 are red, and 2 are green). A) Try to calculate required number of spin for average(μ) loss corresponds to the certain amount of his initial money (M) completely. Around this average loss, what is the confidence interval (95% or μ±2σ ) of the money (the variance (σ2 ) of the process should be calculated as well)?b)RV x is money (won (n times) or lost(N-n times) amount where N is number of spin, e. G. 25, 50, 100, 200, 400, 500,. 1500…) try to establish a distribution and all moments of this RV. Try to explain whether his decision is sustainable or not. Try to find a winning strategy. Plot the probability density function for various N values.

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saishreechandan907 saishreechandan907 · Answer 1 · 2024-05-13T14:39:09-04:00

To calculate the required number of spins for the average loss corresponding to a certain amount of initial money, we need to consider the probability of losing on each spin.

In the game of roulette, there are 18 black slots out of 38 total slots. Therefore, the probability of losing on any given spin when betting on black is 18/38.

Let's assume the initial amount of money the gambler has is M. On each spin, the gambler bets the entire amount on black.

The expected value (average) loss per spin can be calculated as follows:

Expected loss per spin = Probability of losing * Amount bet

= (18/38) * M

= 9M/19

To calculate the average loss corresponding to the initial amount of money (M), we divide the initial amount by the expected loss per spin:

Average loss = M / (9M/19)

= 19/9

Therefore, the required number of spins for the average loss to correspond to the initial amount of money is approximately 19/9 spins.

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