Among people who are infected with Enterobacter, the probability that they have

Question

Among people who are infected with Enterobacter, the probability that they have been recently treated with antibiotics is 0.80, the probability that their infection is resistant to antibiotics is 0.30, and the probability of both is 0.28. Find the probabilities that

(a) such a person has an infection that is resistant to antibiotics, given that they have been treated recently with antibiotics.

(b) such a person has an infection that is resistant to antibiotics, given that they have not been treated recently with antibiotics

(show full solution)

Explanation / Answer

From information given, P(TA)=0.80, P(RA)=0.30, P(TA AND RA)=0.28, where, TA, RA denote events people infected with Enterobacter infection is treated with antibiotics, people infected with Enterobacter infection is resitant to antibiotics.

Use conditional probability formula to find probability of the event B given event A as follows.

P(B|A)=P(A AND B)/P(A)

a. P(RA|TA)=P(TA AND RA)/P(TA)

=0.28/0.80

=0.35 (ans)

b. P(RA|TAc)=P(RA AND TAc)/P(TAc)

=(0.30*0.20)/0.20

=0.30 (ans)

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