A common casino game is roulette. The game is played by throwing a ball on to a
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Question
A common casino game is roulette. The game is played by throwing a ball on to a spinning wheel, known as a roulette wheel. The ball randomly stops on a specific location of the wheel. The ball is equally likely to stop on all locations. That is. the probability of the ball stopping on location, p(i) is equal across all locations. Moreover, the outcomes of each spin of the wheel are independent from one another. The game is played by people placing bets before the ball is thrown on the location of the ball when it stops. The standard wheel has the following properties. The locations are numbered from 0 - 36. 18 locations are black in colour 18 locations are red in color 1 location, "0", is green in color A popular bet is to bet on the color of the location that a ball will land on. What is the probability that the ball will land on a red location? What is the probability that the ball will land on a black location? Another popular bet is to bet on the ball landing on a specific number, say 16. What is the probability that the ball will land on location #16? You have just watched the wheel spin. The wheel landed on location #16. What is the probability that the ball will land on location #16 on the next spin, given that it has just landed on that spot? What is the probability that the ball will land on a red location two spins in a row? While the standard wheel has, locations numbered 0-36. there is a second type of roulette wheel, called an American Wheel. The American wheel has an additional location "00" which is also green. All the other locations are the same. Are you more likely to win a bet on the standard wheel or on the American wheel?Explanation / Answer
Total No . of locations = 37
Red or Black
Probability of ball will land on red location = No. of red locations / Total no. of locations = 18/37 = 0.4865
Probability of ball will land on black location = No. of black locations / Total no. of locations = 18/37 =0.4865
Your favourite number
Probability of ball will land on location #16 = No. of locations 16 / Total no. of locations = 1/37 =0.027
A second spin
A wheel(ball) landed on #16, Probability that the ball will land on location #16 on the next spin
= No. of locations 16 / Total no. of locations = 1/37 = 0.027; Because of the outcomes of each spin of the wheel are independent of one another i.e the outcome of the previous spin does not have any influence(or dependence) on the outcome of the current spin
Two spins
Probability that the ball will land on a red location two spins in row =
P(Probability that the ball landing on a red location in first spin) X P(Probability that the ball landing on a red location in second spin)
= 18/37 x 18/37 =0.2367
Standard vs Americian wheel.
you are more likely to win on the standard wheel
As additional location "00" which also green is added the number of total outcomes are increased from "37" to "38"
The denominator for calculating the probabilities for standard wheel = 37 where as
The denominator for calculating the probabilities for american wheel = 38
Ass denominator increases the value decreases,
The probabilities of winning in American wheel decreases as compared to the standard wheel.
so, you are more likely to win on the standard wheel
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