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

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