Question

9. In a large city, 82% of residents own a cell phone. Suppose that we randomly select three city residents. What is the probability that at least one of the three residents does not own a cell phone? [The city is large enough so that we can assume independence].

A. 0.994

B. 0.449

C. 0.006

Answer 1

Solution:

Probability of "residents own a cell phone" = 82% = 0.82

So , Probability of "residents does NOT own a cell phone" 1 - 0.82 = 0.18

n = 3

X be the number of  residents does not own a cell phone.

X follows Binomial(3 , 0.18)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Find P(At least one of the three residents does not own a cell phone)

= P(X 1)

= 1 - P(X < 1)

= 1 - P(X = 0)

= 1 - { (₃ C ₀) * 0.180* (1 - 0.18)^{3 - 0} }

= 1 - 0.551

= 0.449

Answer : 0.449