Question

Two major cities are connected by a three-lane highway in each direction. Let E1, E2, and E3 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(E2 /E1) =0,8 ,PE3 /E2) =0,9 ,P(E3 /E1) =0,5 ,and P(E3 /E1 E2) =0,9

(a) What is the probability that the highway in each direction will need major repairs next year?

(b) If the need for repair in each direction is statistically independent, what is the probability that the highway will need major repair next year?

Answer 1

(a)

"a) P(E_1 intersection E_2 intersection E_3) = P(E_3