SOLUTION: Hello Disease 1 and Disease 2 are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease 1 sometime during their lifetime

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Question 349808: Hello
Disease 1 and Disease 2 are prevalent among people in a certain population. It is assumed that 10% of the population will contract disease 1 sometime during their lifetime, 15% will contact disease 2 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 contact both diseases, given that he or she has contracted at least disease.

Thank You
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) Hint: P(Contract at least one disease) = P(Contract Disease 1) + P(Contract Disease 2) - P(Contract both diseases)

b) Hint: P(Contract both given having contracted at least one) = P(Contracting both) divided by P(Contract at least one disease)