Question

In New Mexico, about 70% of drivers who are arrested for driving are convicted what is the probability that exactly 11 out of 15 independent selected drivers are convicted?

a) 0.512

b) 0.1916

c) 0.311

d) 0.219

Answer 1

Solution

Given that ,

p = 0.70

1 - p = 1 - 0.70 = 0.30

n = 15

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 11) = (₁₅ C ₁₁) * (0.70)¹¹ * (0.30)⁴

= 0.2186

Probability = 0.219

correct option is = d.