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When Amazon ships a package to a customer, it eventually arrives at the correct destination 94%...

When Amazon ships a package to a customer, it eventually arrives at the correct destination 94% of the time. In the shipping process a package has to be forwarded to a different address 10% of the time, in which case it eventually arrives at the correct destination only 80% of the time. If a randomly selected package does not need to be forwarded, what is the probability that it arrives eventually at the correct destination?

math   Statistics-And-Probability   
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Answer #1

P(correct destination) = 0.94

P(forwarded) = 0.10

P(not forwarded) = 1 - 0.10 = 0.90

P(correct destination | forwarded) = 0.08

P(forwarded and reaches correct destination) = 0.1 x 0.8 = 0.08

P(arrives at correct destination) = P(not forwarded and correct destination) + P(forwarded and correct destination)

0.94 = P(correct destination | not forwarded) x 0.9 + 0.08

P(correct destination | not forwarded) x 0.9 = 0.86

P(correct destination | not forwarded) = 0.9555

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