Two major cities are connected by a three-lane highway in each direction. Let E_

Question

Two major cities are connected by a three-lane highway in each direction. Let E_1, E_2, and E_3 denote the right-hand, center, and left-hand lane, respectively. Upon inspection, the maintenance engineer concludes that the probability that each of these three lanes will require major repair work in the next year are 0.10, 0.05, and 0.01, respectively. From past experience, the following information is available: P(E_2 | E_1) = 0.8, P(E_3 | E_2) = 0.9, P(E_3 | E_10 = 0.5, and P(E_3 | E_1 E_2) = 0.9 What is the probability that the highway in each direction will need major repairs next year? If the need for repair in each direction is statistically independent, what is the probability that the highway will need major repair next year?

Explanation / Answer

The probability of repair in each direction should be the product of individual probabilities:

=0.1*.05*.01 = 0.00005

For conditional probability one can use Bayes theorem i.e.

P(E1 | E2, E3) = P (E1 , E2, E3) / P(E2, E3)

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