SOLUTION: Diseases A and B are prevalent among people in a certain population. It is assumed that 18% of the population will contract disease A sometime during their lifetime, 24% will con

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Question 1188784: Diseases A and B are prevalent among people in a certain population. It is assumed
that 18% of the population will contract disease A sometime during their lifetime,
24% will contract disease B eventually, and 13% will contract both diseases. Find the
probability that a randomly chosen person from this population will contract
(a) at least one disease [2]
(b) exactly one of the diseases [3]
(c) at most one disease
Answer by ikleyn(52878) About Me  (Show Source):
You can put this solution on YOUR website!
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Diseases A and B are prevalent among people in a certain population. It is assumed
that 18% of the population will contract disease A sometime during their lifetime,
24% will contract disease B eventually, and 13% will contract both diseases. Find the
probability that a randomly chosen person from this population will contract
(a) at least one disease
(b) exactly one of the diseases
(c) at most one disease
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(a)  at least one disease is the set (A U B).

         P = P(A U B) = P(A) + P(B) - P(A and B) = 0.18 + 0.24 - 0.13 = 0.29.    ANSWER



(b)  exactly one of the diseases is the set (A U B) minus (A and B).

         P = P(A U B) - P(A and B) = 0.29 - 0.13 = 0.16.                         ANSWER



(c)  at most one means "no one or exactly one". Use the probability values found above in (a) and (b)

         P = (1 - 0.29) + 0.16 = 0.87.                                          ANSWER


     Notice that 0.87 is exactly the same as  1 - 0.13.

Solved and explained.