Question

An American roulette wheel has 38 slots and 18 of these are red. After 190 spins, what is the probability it will land on red 78 or fewer times

Answer 1

0.040563

Explanation:

Given that:

Total Number of slots = 38

Number of red slots = 18

Number of spins (n) = 190

p = p(red) = 18/38 = 0.473684

Using Normal approximation :

Mean(m) = np = 190 * 0.473684 = 90

Standard deviation = √n*p*(1-p)

Standard deviation = √90 * 0.5263157

Standard deviation(σ) = 6.88

Probability of landing on red 78 or fewer times :

Zscore = (x - m) / σ

Zscore = (78 - 90) / 6.88

Zscore = - 12 / 6.88

Zscore = - 1.744186

P(Z < - 1.744186) = 0.040563