Consider the following system:

-> 0.73 -> 0.73 ->

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

(Round your final answers to 4 decimal places, not your intermediate calculations.)

a.) The system as shown

b.) Each system component has a backup with a probability of .73 and a switch that is 100% percent reliable.

c.) Backups with .73 probability and a switch that is .98 percent reliable.

My answers:
a.) 0.5329
b.) 0.8595
c.) 0.8542

Concern & Question:

Problem C.) ~ I calculated this problem by
1-.73= .27
1-.73= .27
1-.98= .02

.27*.27*.02= .001458
1-.001458= .8542

Did I calculate this problem (C.) correctly?
If not, how do I calculate this problem?
(Step by step, please...) and what should be the answer?

Thank you so much for your help!

Well, your calculations seem to be on the right track, but there's just a slight mistake. When determining the probability of the backup component failing, you would actually multiply 1 - 0.73, which gives you 0.27. Then, when determining the probability of the switch failing, you would multiply 1 - 0.98, which gives you 0.02.

So, your new calculation for problem c. would be:

0.27 * 0.27 * 0.02 = 0.001458

Now, to find the overall probability of the system operating in this condition, you subtract the result from 1. So:

1 - 0.001458 = 0.998542

Rounding this to four decimal places, the answer for problem c. would be 0.9985.

I hope that clears things up for you!

To calculate the probability in problem C, where each system component has a backup with a probability of 0.73 and a switch that is 0.98 reliable, you need to consider the different scenarios in which the system may fail.

Step-by-step calculation:

1. Calculate the probability that the first component fails (1 - 0.73) = 0.27.
2. Calculate the probability that the second component fails (1 - 0.73) = 0.27.
3. Calculate the probability that the switch fails (1 - 0.98) = 0.02.

Now, consider the scenarios in which the system can fail:

1. Both components and the switch fail:
Probability = 0.27 * 0.27 * 0.02 = 0.001458.

2. Subtract the probability of failure from 1 to get the probability of the system operating:
Probability = 1 - 0.001458 = 0.998542 (rounded to 4 decimal places).

Therefore, the correct answer for problem C is 0.9985, not 0.8542 as you mentioned.

You calculated the individual failure probabilities correctly, but you made a mistake on the final step by subtracting the probability of failure from 1 instead of subtracting it from the probability of success to get the correct answer.

So, the correct answer for problem C is 0.9985.

Your calculation for problem C is correct. Here's the step-by-step calculation for problem C:

1. Calculate the probability of one component failing (since the probability of success is given as 0.73, the probability of failure is 1 - 0.73 = 0.27).
2. Calculate the probability of the backup component failing (0.27).
3. Calculate the probability of the switch failing (since the probability of reliability is given as 0.98, the probability of failure is 1 - 0.98 = 0.02).
4. Multiply the probabilities of all three failures together: 0.27 * 0.27 * 0.02 = 0.001458.
5. Calculate the probability of the system operating by subtracting the probability of all failures from 1: 1 - 0.001458 = 0.998542.

So, the probability that the system will operate under the conditions of having backups with a probability of 0.73 and a switch that is 0.98 percent reliable is 0.8542 (rounded to 4 decimal places).