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30 Apr 2019, 00:58
Kudos
Bookmarks
Hello everyone, could you please help me with solving the below 2 question?
A machine has 4 components A, B, C and D. The raw material is the input to the component A; if the component A works, its output automatically becomes the input to the component B; again if the component B works, its output becomes the input to the component C; if the component C works, its output becomes the input to the component D; finally if the component D works, its output is the final product. If at any stage, the component under consideration fails, we say that the machine fails. The component A fails 1% of the times. Given that A works, B fails 2% of the times. Given that A and B work, C fails 3% of the times. Finally, given that A, B and C work, D fails 4% of the times.
1. What is the probability that the machine fails?
a. 0.1
b. 0.09244976
c. 0.09654976
d. 0.09564046
2. Given that the machine fails, what is the probability (correct to 6 places of decimal) that it fails
at the third stage (that is C fails when its turn comes)?
a. 0.301461
b. 0.029106
c. 0.030001
d. None of the above
Thank you in advance!
Sent from my ONEPLUS A5000 using GMAT Club Forum mobile app
A machine has 4 components A, B, C and D. The raw material is the input to the component A; if the component A works, its output automatically becomes the input to the component B; again if the component B works, its output becomes the input to the component C; if the component C works, its output becomes the input to the component D; finally if the component D works, its output is the final product. If at any stage, the component under consideration fails, we say that the machine fails. The component A fails 1% of the times. Given that A works, B fails 2% of the times. Given that A and B work, C fails 3% of the times. Finally, given that A, B and C work, D fails 4% of the times.
1. What is the probability that the machine fails?
a. 0.1
b. 0.09244976
c. 0.09654976
d. 0.09564046
2. Given that the machine fails, what is the probability (correct to 6 places of decimal) that it fails
at the third stage (that is C fails when its turn comes)?
a. 0.301461
b. 0.029106
c. 0.030001
d. None of the above
Thank you in advance!
Sent from my ONEPLUS A5000 using GMAT Club Forum mobile app
Archived Topic
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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02 May 2019, 20:41
Kudos
Bookmarks
1. Probability that the machine fails
= (A fails) OR (A works, but B fails) OR (A and B work, but C fails) OR (A, B, and C work, but D fails)
= 0.01 + 0.99 * 0.02 + 0.99 * 0.98 * 0.03 + 0.99*0.98*0.97*0.04
= 0.09654976
Option (C).
2. Probability that the machine fails at the third stage
= A and B work, but C fails
= 0.99 * 0.98 * 0.03
= 0.029106
Option (B)
= (A fails) OR (A works, but B fails) OR (A and B work, but C fails) OR (A, B, and C work, but D fails)
= 0.01 + 0.99 * 0.02 + 0.99 * 0.98 * 0.03 + 0.99*0.98*0.97*0.04
= 0.09654976
Option (C).
2. Probability that the machine fails at the third stage
= A and B work, but C fails
= 0.99 * 0.98 * 0.03
= 0.029106
Option (B)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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