Problem 1

During blood testing a sample of five donor’s blood donations are combined into one vial for the purpose of testing for disease.  If the vial tests negative, all five donations can be used for blood transfusions.  If the vial tests positive, all five donations individually must be tested to determine which of the five donations are contaminated.  If the rate of disease in the population is 1%, what is the probability that all five donations will need to be tested individually?