I was trying to solve this problem. There are three roads that connected town A to town B. road 1 and road 2 have 2 sections, and road 3 has 1 section. The probability that a section will be blocked will bee equal to p, and 0
The road would be blocked if either one of the section is blocked or two sections are blocked.
The blocking of road would happen independent of each other, and the probability of choosing road is uniformly distributed.
I tried to solve this problem by listing the case:
P( road 1 is chosen and it is not blocked, and road 2 and 3 are blocked 丨road 1 is chosen and it is not blocked )
P(Road 2 chosen and it is not blocked, and road 1 and 3 are blocked 丨 road 2 is chosen and it is not blocked)
P(Road 3 chosen, and it is not blocked and road 1 and 2 are blocked 丨 road 3 chosen and it is not blocked)
Then, adding the probability up. However, the answer I got is not correct.
The answer indicated that I should give the probability like:
P(random road chosen and chosen road open and unchosen road blocked 丨 chosen road open)
I want to know why it is different from the actual answer
Thank you very much for your reply
Update: I really don't know whether my title of question links correctly to the content, I am very sorry for confusion. Please point out any error