Question

2. Suppose that in a certain country, 10% of the elderly people have diabetes. It is also known that 30% of the elderly people are living below poverty level, and 35% of the elderly population falls into at least one of these categories. A. What proportion of elderly people in this country have both diabetes and are living below poverty level? b. Suppose we choose an elderly person in this country ”at random.” What is the probability that the person will neither have diabetes nor be living at the poverty level?

Answer 1

Given,

P(Diabetes) = 0.10 , P(below poverty level) = 0.30

P(Diabetes or below poverty level) = 0.35

a)

We have to calculated P( Diabetes and below poverty level) = ?

Using formula P(A or B) = P(A) + P(B) - P(A and B)

P(Diabetes or below poverty level) = P(Diabetes) + P(below poverty level) - P( Diabetes and below poverty level)

0.35 = 0.10 + 0.30 - P( Diabetes and below poverty level)

So,

P( Diabetes and below poverty level) = 0.10 + 0.30 - 0.35

= 0.05

b)

P(neither diabetes nor at poverty level) = 1 - P(Diabetes or below poverty level)

= 1 - 0.35

= 0.65