Question

The probability that a unit of blood was donated by a paid donor is 0.75. If the donor was paid, the probability of contracting serum hepatitis from the unit is 0.016. If the donor was not paid, this probability is 0.001.

(a) A patient receives a unit of blood. What is the probability of the patient contracting serum hepatitis from this source?

(b) A patient contracts serum hepatitis from a unit of blood he received. What is the probability that the blood was donated by a paid donor?

Answer 1

contracting serum hepatitis from the unit 0.016 paid donor 0.984 \ not contracting serum hepatitis from the unit 0.75 contracting serum hepatitis from the unit 0.001 0.25 non- paid donor not contracting serum hepatitis from the unit 0.999

a) the probability of the patient contracting serum hepatitis from this source=$=0.75*0.016+0.25*0.001=0.0123$

b)this can be solved using Bayes theorem

the probability that the blood was donated by a paid donor=$=\frac{0.75*0.016}{0.75*0.016+0.25*0.001}=0.9796$