Question

solve In 2010, the percentage of assisted living residents who had both heart disease and depression was 9%, the percentage with only heart disease was 25%, and the percentage with either condition was 48%. What percentage of assisted living residents had only depression

Answer 1

The percentage of assisted living residents had only depression

P(D) =0.32

Explanation:

Explanation:-

Given the percentage of assisted living residents who had both heart disease and depression was 9%

Let The event 'H' be the event of heart disease and 'D' be the event of depression

P(H ∩D) = 9% =0.09

The percentage with only heart disease was 25%

P(H) = 0.25

The percentage with either condition was 48%.

P(H∪D) = 48%=0.48

By addition theorem on probability

`P(H UD) = P(H) +P(D) - P(H n D)`

`0.48 = 0.25 + P(D) -0.09`

P(D) = 0.48 -0.16

P(D) = 0.32

The percentage of assisted living residents had only depression

P(D) =0.32