Question

A roulette wheel has 2 green spaces, 18 red, and 18 black spaces. If the wheel is spun 5 times, and if the outcomes of individual spins are all independent,

If we define the random variable x to be the number times that red shows up from any 5 spins, what can we know about X

Answer 1

The probability of getting a red in any spin is computed here as:
= Total number of red spaces / Total number of spaces

= 18/38

The number of times that red shows up out of the 5 spins is modelled here as:

Therefore it is a binomial distributed random variable with parameters n = 5 and probability of success here as 18/38.

Note that it is binomial distribution because of the following reasons:

• We are given that each trial is independent of each other here.
• There are only two outcomes in each trial: Red space or non Red space. Note that non red space could be either red or green space but we take both of them equivalent here.
• Also the probability of getting red space in each trial is same.