Question

1 point) during a winter season at one ski resort, there are two roads from area a to area b and two roads from area b to area
c. each of the four roads is blocked by snow with a probability of 0.25, independently of the other roads. 1. what is the probability that there exists an open route from area a all the way to area c

Answer 1

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