Question

Question 1: In the casino game Roulette, a bet on “red” will win if the ball lands on one of the 18 red numbers of the 38 numbers on the wheel, with each number being equally likely. You want to run a simulation that will estimate the probability of a player winning both bets when betting on red twice. Which of the following would be an appropriate setup for the simulation:

I. Use a table of random digits to select one number from 01 to 38 and then a second number from 01 to 38. If the first number is between 01 and 18 and the second number is between 01 and 18, then the player has won both rounds.

II. Use a table of random digits to select two numbers 01-38, without repeats. If both numbers are between 01 and 18, then the player has won both rounds.

III. Use a table of random digits to select two numbers 01-19, allowing repeats. If both numbers are between 01 and 09, then the player has won both rounds.

A) I

B) II

C) III

D) I and II

E) I and III

Answer 1

Since all the 38 numbers on the wheel are equally likely hence we may assume that the 1st 18 of them are red and rest 20 are non-red numbers.
Now the ball may land on the same number twice. Hence if we select 2 random numbers without a replacement that will be totally incorrect because the same random number will never appear twice, but the ball can land on the same number twice. Hence the second setup is removed from the situation.

Next, selecting two random numbers from 1 to 38 with replacement is the same as selecting a random number from 1 to 38 and repeating the same process again. in both cases, the same number may appear twice and in both case probability of selecting any number from 1-38 remains the same. Hence both of them are equivalent. therefore appropriate setup is either of the two

I. Use a table of random digits to select one number from 01 to 38 and then a second number from 01 to 38. If the first number is between 01 and 18 ( representing the 18 red coloured numbers ) and the second number is between 01 and 18 ( representing the 18 red coloured numbers ), then the player has won both rounds.

III. Use a table of random digits to select two numbers 01-19, allowing repeats. If both numbers are between 01 and 09, then the player has won both rounds.

Answer E) I and III