Diseases I and II are prevalent among people in a certain population. It is assu
ID: 2959113 • Letter: D
Question
Diseases I and II are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease I sometime during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases.a. Find the probability that a randomly chosen person from this population will contract at least one disease.
b. Find the conditional probability that a randomly chosen person from this population will contract both diseases, give that he or she has contracted at least one disease.
c.What is the probability that a randomly selected person from this population will not contract any diseases?
Explanation / Answer
Given
P(disease A)=0.1
P(disease B) = 0.11
P(both)=0.04
-------------------------------------------------------------------------------------------------------------
(a) P(at least one disease)
=P(disease A) + P(disease B) - P(both)
=0.1+0.11-0.04
=0.17
-------------------------------------------------------------------------------------------------------------
(b)P(both | at least one disease)
=P(both) / P(at least one disease)
=0.04/0.17
=0.2352941
-------------------------------------------------------------------------------------------------------------
(c)P(will not contract any diseases)
=1-P(at least one disease)
=1-0.17
=0.83