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In: Math

James travels from Toronto to Calgary then Vancouver and finally to Prince George. There is a...

James travels from Toronto to Calgary then Vancouver and finally to Prince George. There is a 5% chance that his luggage is left behind in Toronto. If it is not left behind in Toronto, there is a 7% chance that it is left behind in Calgary. If it not left behind in Toronto or Calgary, there is a 10% chance that it is left behind in Vancouver. What is the probability his luggage is lost?

Solutions

Expert Solution

Let A be the event that the luggage is left behind in Vancouver, B be the event it is left behind in Calgary and C be the event it is being left behind in Toronto.

We have, P(C) = 0.05 i.e. P() = 1 - 0.05 = 0.95,

P(B | ) = 0.07 i.e. P( | ) = 1 - 0.07 = 0.93 i.e. P() = 0.93 * P() = 0.93 * 0.95 = 0.8835

and P(A | ) = 0.10 i.e. P( | ) = 1 - 0.10 = 0.90 i.e. P() = 0.90 * P() = 0.90 * 0.8835 = 0.7952

Thus, the probability that the luggage is lost = 1 - The probability that the luggage is not lost = 1 - P() = 1 - 0.7952 = 0.2048 (Ans).

milcah answered 2 days ago
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