Question

Three highways connect city A with city B. Two highways connect city B with city C. During a rush hour, each highway is blocked by a traffic accident with probability 0.2, independently. What is the probability that there is at least one blocked highway between city A and city C?

1) 0.04
2) 0.16
3) 0.36
4) 0.64

Answer 1

The probability that there is at least one blocked highway between city A and city C is 0.7379.

Step-by-step explanation:

To find the probability that there is at least one blocked highway between city A and city C, we can use the concept of complement. Let's find the probability that none of the highways between city A and city C are blocked.

Since there are three highways connecting city A with city B and two highways connecting city B with city C, the total number of possible combinations of highways is 3 * 2 = 6.

The probability that any given highway is blocked is 0.2, so the probability that it is not blocked is 1 - 0.2 = 0.8. Since the events of each highway being blocked or not blocked are independent, the probability that none of the highways are blocked is (0.8)^6 = 0.2621.

Therefore, the probability that there is at least one blocked highway between city A and city C is 1 - 0.2621 = 0.7379.