Question

In the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 38 times, find the probability of the following events.

A. The ball falls into the green slots 4 or more times.

B. The ball does not fall into any green slots.

C. The ball falls into black slots 15 or more times.

D. The ball falls into red slots 10 or fewer times.

Answer 1

Given:

n = 38

Total slots = 18+18+2 = 38

Now ,

The probability of green slots

P(green slots) = 2/38 = 0.0526

Let X be the number of green slots.

X follows the Binomial distribution.

X ~ Binomial(n,p)

Therefore

a) The ball falls into the green slots 4 or more times is 0.1377

b) The ball does not fall into any green slots is 0.1283

c) The ball falls into black slots 15 or more times is 0.8726

D. The ball falls into red slots 10 or fewer times is 0.0066

All answer rounded to 4 decimal place.