The time, t, in minutes, between successive arrivals at an emergency room of a certain city hospital on Saturday nights can be described by the function E(t) = 0.2e^-0.2t when t> or equal to 0. Two patients arrive at the emergancy room every 10 minutes.

(a) Calculate the probability that successive arrivals are between 20 and 50 minutes apart. (Round your answer to four decimal places.).

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(b) Calculate the probability that 10 minutes or less elapses between successive arrivals. (Round your answer to three decimal places)

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(c) Calculate the probability that successive arrivals will be more than 5 minutes apart. (Round your answer to three decimal places)

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Please fill in the blanks and state answers clearly! Thank you!!