[Rates and Probabilities] Suppose the three-year probability of getting the flu, if you are unvaccinated, is 65.7%, and that the incidence rate (1-year rate) is constant over those three years.

a. Calculate the 1-year incidence rate using the appropriate formula. (That formula is r = -ln(1 - p)/t ). Show your work. Have your answer correct to four decimal places (e.g. 0.1234). This is to make sure your answer to part b. is accurate. Rate: ________________

b. Calculate the 1-year probability of getting the flu, using the rate you calculated in part a. (That formula is p = 1 - e^(-rt) , which is just the formula mentioned in part a, rearranged to have p on the left.) Show your work. Have your probability correct to two decimal places (e.g. 33.33%). Hint: You can double-check your work using standard probability math. If the one-year probability of getting sick is S, then the probability of getting sick within a three year window is the probability of getting sick in Year 1, S, plus the probability you didn't get sick in year 1, but did get sick in year 2, (1 - S) x S, plus the probability you didn't get sick in years 1 or 2, but did get sick in Year 3, (1 - S) x (1 - S) x S. Probability: ______________ %