Question

In a clinical group 30% has heart disease, 45% has diabetes, and has 15% has both heart disease and diabetes. a) What is the probability that a randomly selected person in the group has diabetes, knowing that he has heart disease? b) Are the events ‘having diabetes’ and ‘having heart disease’ disjoint? Explain your reasoning. c) What percent of the population has either diabetes or heart disease?

Answer 1

Let H be the event that the selected person has heart disease.

Let D be the event that the selected person has diabetes.

Now according to the question:

P(H) = 0.30

P(D) = 0.45

P(H D) = 0.15

a)

We have to find the probability:

P(D/H)

= P(H D) / P(H)

= 0.15 / 0.30

= 0.5

b)

No, the events ‘having diabetes’ and ‘having heart disease’ are not disjoint since P(H D) = 0.15. Two event are disjoint if and only if H D = Ф and P(H D) =0. Since this is not the case here, the given events are not disjoint.

c)

We have to find P(H D)

= P(H) + P(D) - P(H D)

= 0.30 + 0.45 - 0.15

= 0.60

60% population has either diabetes or heart disease.

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