Question

6. Of all people in one population, 21% have high blood pressure and 36% are overweight. In addition, 42% of people who are overweight also have high blood pressure. Let H represent the event that a person has high blood pressure, and O represent the event that a person is overweight. In each part of this question, you must first express each probability in terms of the events Hand O and justify any computation through the use of a formula. (a) Express each of the three probabilities listed above in terms of the events H and 0. (b) Are H and independent events? Explain your answer using only the probabilities stated in part (a). (c) What proportion of all people are not overweight? (d) What is the probability that a randomly selected person will have high blood pressure and be overweight? Are H and O mutually exclusive events? Explain. (e) What is the probability that a randomly selected person will have at least one of these two conditions? (f) What proportion of all people have high blood pressure but are not overweight? (g) If a person has high blood pressure, what is the probability they are also overweight?

Answer 1

a) Based on the above percentage, we find,

P(H) = 0.21 and P(O) = 0.36

P(H and O) = 0.42*0.36= 0.1512

b) Two events A and B are said to be independent if,

P(A and B) = P(A)*P(B)

Here, P(H and O) is not equal to P(H)*P(O)

So H and O are not independent

c) Proportion of people not overweight= 1- proportion of people who are overweight = 1-0.36= 0.64

d) Here we want, P(H and O) = 0.1512

Two events are said to be mutually exclusive if the occurrence of one does not affect the occurrence of another. Here this is not the case as 42% of overweight people have high blood pressure.

So H and O are not mutually exclusive.