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

0.040563

Step-by-step 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