Answer to Question #102368 in Statistics and Probability for C

Question

About 50% of all persons age 3 and older wear glasses or contact lenses. For a randomly selected group of five people, compute the probability that
a- exactly three wear glasses or contact lenses
b- at least one wears them
c- at most one wears them

Answer 1

This is a binomial distribution with p=0.5, q=1-p ; q=1-0.5=0.5 and n=5

P(x)= (nCx) * px q(n-x)

a) exactly 3 wearing glasses or contact lenses

P(x=3)

=(5C3)*0.5^3*0.5^2

=0.3125

b) at least one wears

p(x≥1)= 1-p(x=0)

= 1- (5C0)*0.5^0*0.5^5

=1-0.03125

=0.96875

c) at most one wears

p(x≤1)= p(x=0)+p(x=1)

={(5C0)*0.5^0*0.5^5}+{(5C1)*0.5^1*0.5^4}

=0.1875