SOLUTION: 50% of American population is overweight. 65% of American population develops heart disease 57% of those overweight get heart disease What is the probability of being overweight

Question 31638: 50% of American population is overweight.
65% of American population develops heart disease
57% of those overweight get heart disease
What is the probability of being overweight or having heart disease.
Answer by mbarugel(146) (Show Source): You can put this solution on YOUR website!
Hello!
The rule we must use here is this:
Given two events, A and B, then:
Prob(A or B) = Prob(A) + Prob(B) - Prob(A and B)
Let's call A to the event that someone is overweight, and B to the event that someone has a heasrt disease. From the problem, we already know:
Prob(A) = 0.50
Prob(B) = 0.65
We now need to find Prob(A and B). For that, we use the last piece of information: 57% of those overweight get heart disease. The overweight percentage is 50% Therefore, 57% of the 50% have a heart disease and are overweight. 57% of 50% is 0.57*0.50 = 0.285. Therefore,
Prob(A and B) = 0.285
We conclude that:
Prob(A or B) = Prob(A) + Prob(B) - Prob(A and B) = 0.50 + 0.65 - 0.285 = 0.865 = 86.5%

I hope this helps!
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