Answer: plan B is better
Explanation:
Machines _____reliability
__A__________ 0.99
__B__________ 0.96
__C__________ 0.93
Backup machines A, B, C also have similar probabilities :
PLAN 1:
P(success) = 0.99 * 0.96 * 0.93 = 0.8839
P(line fails) = 1 - 0.8839 = 0.1161
P(backup) = 0.99 * 0.96 * 0.93 = 0.8839
P(success) + [p(line fails) * p(backup)]
0.8839 + (0.1161 * 0.8839)
0.8839 + 0.10262079
= 0.9865
Plan B:
Backup is provided for each machine ;
P(success) + [p(line fails) * p(backup)] for each of machine A, B and C
Machine A:
0.99 + (1 - 0.99)*0.99 = 0.9999
Machine B:
0.96 + (1 - 0.96)*0.96 = 0.9984
Machine C:
0.93 + (1 - 0.93)*0.93 = 0.9951
A*B*C = 0.9999 * 0.9984 * 0.9951 = 0.9934
Plan B has greater probability of success.
2.) plan A provides a central or one single backup option should any of the machines fail. However, plan B provides separate backup options for each of machines A, B and C.
3.) choosing a plan may also depend on the cost of providing each backup plan.
