Question

In the game of​ roulette, a wheel consists of 38​ slots, numbered​ 0, 00,​ 1, 2,​ ..., 36. To play the​ game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numbered 0 and 00 are​ green, the odd numbers are​ red, and the even numbers are black. To simulate outcomes from spinning the​ wheel, a researcher used the integer distribution to randomly generate 1000 numbers from 1 to​ 38, where 37 represents 0 and 38 represents 00.

Required:
a. What is the probability that the metal ball lands on green or red?
b. What is the probability that the metal ball does not land one green?

Answer 1

The probability of the metal ball landing on green or red is 10/19, while the probability of it not landing on green is 18/19.

Step-by-step explanation:

a. The probability of the metal ball landing on green or red is the sum of the individual probabilities. There are two green slots out of a total of 38 slots, so the probability of landing on green is 2/38. There are 18 red slots out of a total of 38 slots, so the probability of landing on red is 18/38. Therefore, the probability of landing on green or red is (2/38) + (18/38) = 20/38, which can be simplified to 10/19 or approximately 0.526.

b. The probability of the metal ball not landing on green can be calculated by subtracting the probability of landing on green from 1. The probability of landing on green is 2/38, so the probability of not landing on green is 1 - (2/38) = 36/38, which can be simplified to 18/19 or approximately 0.947.