Probability of accessibility Between A, B, and C, there are the following highways:
A – B, A – C, and B – C. During monsoon, when there is heavy rain, each of the road gets blocked independently with probability $p$.
What is then the probability that C will be accessible from A?
I'd say the probability is 1/3, since there's 3 roads that could be blocked off? Am I correct in that assumption?

Path A-B-C is free when A-B and B-C is free:
$p_{ABC-free} = (1-p)*(1-p)= (1-p)^2$
So it is blocked:
$p_{ABC-blocked} = 1-p_{ABC-free} = 1-(1-p)^2= 1-1+2p-p^2 = p(2-p)$
C is not accessible from A if ABC and AC is blocked:
$p_{blocked} = p_{ABC-blocked} * p_{AC-blocked} = p(2-^2) p = p^2(2-p)$
So it is possible to move from A to C with probability
$p_{free} = 1-p_{blocked} = 1- p^2(2-p)$
Check it out:
if p=0: 
$p_{free} = 1-0 = 1$
if p=1: 
$p_{free} = 1-1\cdot 1 = 0$
if p =0.5:
$p_{free} = 1- 0.5^2(2-0.5) = 1-0.25\cdot 1.5 = 0,625$
You can see. Here with probability of 0.5 you can travel A-C. But with probability 0.5 you can't. There you have a chance of 0.5*0.5 that bot ways are accessable.
