Question

A roulette wheel has 38 spaces: 18 red, 18 black, and 2 green. Suppose that in each spin of the wheel, the ball is equally likely to land on any of the 38 spaces, and that spins are independent. The wheel will be spun five times.

The chance that the ball lands on black in all five spins is closest to
a) 0.688%
b) 6.366%
c) 12.044%
d) 17.722%
e) 23.401%

Answer 1

2.29%

Explanation:

1. Chance of landing on black for one spin:

There are 38 spaces, and 18 lead to the wanted result. That means the chance is ¹⁸/₃₈, or about 0.47.

2. Chance for 5 spins.

We need to find (0.47)⁵, which is about 0.0229, which is 2.29%

That is none of the choices, but from every way I did this problem, that is the only solution I got.