Question

Consider the following system:

→ 0.89 → 0.89 →

Determine the probability that the system will operate under each of these conditions:

a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability:_______

b. Each system component has a backup with a probability of .89 and a switch that is 100% percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability:_________

c. Backups with .89 probability and a switch that is 98 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)

Probability:_____

Answer 1

a) As the given components are in series, probability that the system operates here is computed as:

= 0.89*0.89

= 0.7921

Therefore 0.7921 is the required probability here.

b) Again, here instead of 0.89 probability of reliability for both components, one has a 100% reliability, therefore the probability that the system operates here is computed as:

= 0.89*1

= 0.89

Therefore 0.89 is the required probability here.

c) Similar to the above 2 parts, the probability here is computed as:

= 0.98*0.89

= 0.8722

therefore 0.8722 is the required probability here.