Reference no: EM13960401
Problem: Screening for infectious diseases in a blood-bank setting is a major part of ensuring blood safely. At a local clinic, subject's blood donations are tested for infection. Suppose that 5 percent of all blood donations are infected n some way (e.g., HIV, HCV, syphilis, etc.). For simplicity, assume that all subjects are independent.
(a) Let Y denote the number of subjects tested to find the first infected blood donation. Find P(Y>3). Interpret what this probability means in words.
(b) In par (a), calculate P(Y >5 Y>2). How does this answer compare with P(Y > 3)? Why do you think this is?
(c) Suppose that, during a given day, there are 30 donations. Find the probability that no more than two of these donations are infected.
(d) Of the 30 donations in part (c), 10 donations come for African American (AA) donors and 20 come from non AA donors. If I pick 3 donations at random, what is the probability that exactly one is from AA donor?
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