Question

In one population, it is found that 6% of all people have high blood pressure and 40% are overweight. Four percent suffer from both con- ditions. What is the probability that a randomly selected person from this population will have high blood pressure given that he is not over- weight?

Please explain :)

Answer 1

Let A be the event that a person has high blood pressure

and B be the event that a person is overweight.

Given that, P(A) = 0.06, P(B) = 0.4, P(A B) = 0.04

The probability that a randomly selected person from this

population will have high blood pressure given that he is

not overweight = P(A | ) = P(A ) / P()

Now, P(A) = P(A B) + P(A )

i.e. P(A ) = P(A) - P(A B) = 0.06 - 0.04 = 0.02

Again, P() = 1 - P(B) = 1 - 0.4 = 0.6.

Hence, required probability = 0.02/0.6 = 0.0333. (Ans).