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The U.S. Public Health Service's Advisory Committee on Immunization Practices recommends a tetanus booster every 10 years. Suppose the lifetime (in years) of a tetanus booster shot has an exponential distribution with λ = 0.05.

a. Find the probability that a randomly selected tetanus booster shot is still protecting against tetanus after more than 10 years.

b. Suppose a physician recommends a booster shot after a period when only 10% of all tetanus shots still have an effect. How long should you wait before getting another booster shot?

c. Suppose two people independently receive tetanus shots. What is the probability that both shots still have an effect after more than five years?

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