2 Diseases A and B are prevalent among people in a certain p

2) Diseases A and B are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease A sometime during their lifetime, 11 % will contract disease B eventually, and 4% will contract both diseases. 2a) Find the probability that a randomly chosen person from this population will contract at least one disease. 2b) Find the conditional probability that a randomly chosen person from this population will contract both diseases, given that he or she has contracted at least one disease. 2e) Find the probability that a randomly selected person from this population will not contract any diseases.

Solution

Given

P(disease A)=0.1

P(disease B) = 0.11

P(both)=0.04

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(a) P(at least one disease)

=P(disease A) + P(disease B) - P(both)

=0.1+0.11-0.04

=0.17

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(b)P(both | at least one disease)

=P(both) / P(at least one disease)

=0.04/0.17

=0.2352941

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(c)P(will not contract any diseases)

=1-P(at least one disease)

=1-0.17

=0.83