Probability problem (Bernoulli trial)

Question

I recently became interested in studying probability and I stumbled upon this question:

There are three points: A, B and C. Exactly two paths exist between A and B and exactly two paths exist between B and C. If the probability that each one of these paths is blocked (independently of the other paths) is 0.3, find the probability that at least one non-blocked path exists between points A and C.

My attempt at finding a solution:

Let H1 = there exists a non-blocked path between A and B, and H2 = there exists a non-blocked path between B and C. Then, we can calculate H1*H2 = there exists a non-blocked path between A and C as 0.7 * 0.7 = 0.49.

The final probability, using the Bernoulli trial formula is 0.93234799.

I am not sure if this is correct (my textbook has no solution for this problem), so I'd be really happy if someone could verify the validity of my solution or tell me how to get the right one.

Thanks in advance.

Answer 1

The answer would be $H_1 \cdot H_2$ as you have defined it, but you have computed $H_1$ and $H_2$ incorrectly.

The complement of "there exists a non-blocked path between A and B" is "both paths between A and B are blocked." The latter event has probability $0.3^2=0.09$, so $H_1=1-0.09=0.91$.

I am not sure what you are trying to do with the "Bernoulli trial formula."