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A local courier service sends packages to Oakland and offers a money back guarantee that each package will be delivered within 24 hours. The courier service sends 70% of packages by plane, 20% by train, and10% by van. If a package is sent by airplane, the probability it is delivered within 24 hours is 0.96. For packages sent by train and van, the probability they are delivered within 24 hours are 0.92 and 0.87,respectively.

(a) What proportion of the time will the courier service meet its guaranteed delivery time?

(b) If a package fails to reach Oakland within 24 hours, what is the probability it was sent by train? (with all steps please)

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