Three highways connect city A with city B. two highways connect city B with city C. during rush hours, each highway is blocked by a traffic accident with probability 0.2, independently of other highways.

(a) compute the probability that there is atleast one open route from A to C.

Probability that a highway is blocked = 0.2

Probability that a highway is not blocked = 1 - 0.2 = 0.8

Let x be a random variable representing the number of open highways.

P (x ≥ 1) = 1 - P (x < 1) = 1 - P (0)

P (0) = 5C0 (0.8) ^0 (0.2) ^5 = 1 (1) (0.00032) = 0.00032

P (x ≥ 1) = 1 - 0.00032 = 0.99968

Therefore, the probability that there is atleast one open route from A to C is 0.99968