Diseases I and II are prevalent among people in a certain population. It is assu

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 sometimes during their lifetime, 15% will contract disease II eventually, and 3% will contract both diseases. Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime. Also, Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime.

Explanation / Answer

Given P(I)=0.1 P(II)=0.15 P(I and II)=0.03 ------------------------------------------------------------------------- Find the probability that a randomly chosen person from this population will contract at least one disease in his/her lifetime. P(I or II) = P(I) +P(II) - P(I and II) =0.1+0.15 - 0.03 =0.22 ---------------------------------------------------------------------------- Find the conditional probability that a randomly selected person from this population will contract both diseases, given that he or she has contracted at least one disease in his/her lifetime. P(both)/P(at least one) = 0.03/0.22 = 0.1363

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