Probability that both roads from a to b are blocked is the product of the individual probabilities, i.e. P(~ab)=0.25*0.25=0.0625 Similarly P(~bc)=0.25*0.25=0.0625 Probability that EITHER one or both of ab and bc are blocked is the sum of the probabilities: P(~ab ∪ ~bc)=0.0625+0.0625=0.125 (recall that one cannot travel from a to c if either ab or bc is blocked.)
Therefore the probability that there exists an open route from a to c = P(ac) = 1-P(~ab ∪ ~bc) = 1 - 0.125 =0.875
