Question

Problem 1: Two locations A and B are linked by three different paths. Each path contains number of mobile bridges that can be opened or closed as needed. The numbers in the figure below represents the probability that each bridge will be open. Assume that the bridges operate independently. a) What is the probability that location B is accessible from A (that is, there exist at least one path with no bridge lifted)? b) Suppose you are told that B is accessible from A, what is the probability that the bridge with 40 percent chance of being open is closed?

Answer 1

if pi is probability that bridge will be close
then
for series
p = p1* p2
for parallel
= 1 -(1-p1)(1-p2)

a)
probability that there location B is accessible from A
= 1- (1 - 0.75 * 0.75)(1 - 0.6)(1 - 0.9 * 0.9*0.9)
= 0.952575

b)
P(bridge with 40 % is closed | B is accesible from A)
= P(bridge with 40 % is closed and B is accesible from A) / P(B is accesible from A)
=0.6/0.952575
=0.629871