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Probability of at least one encounter Suppose that in a large group of people, a fraction 0 ≤ r ≤ 1 of the people have flu. The probability that in n random encounters you will meet at least one person with flu is P = f(n, r) = 1 – (1 – r)n. Although n is a positive integer, regard it as a positive real number.
a. Compute fr and fn.
b. How sensitive is the probability P to the flu rate r? Suppose you meet n = 20 people. Approximately how much does the probability P increase if the flu rate increases from r = 0.1 to r = 0 11 (with n fixed)?
c. Approximately how much does the probability P increase if the flu rate increases from r = 0.9 to r = 0.91 with n = 20?
d. Interpret the results of parts (b) and (c).
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