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01 Aug 2020, 06:19
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D
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The electrical apparatus works as long as current can flow from point X to Y. The three components A, B and C are independent. The probability that component A works is 0.8; the probability that component B works is 0.9; and the probability that component C works is 0.75. Find the probability that apparatus(shown below) will work ?
NOTE- If any component doesn't work, current will not pass through it.
A. 0.54
B. 0.75
C. 0.8
D. 0.93
E. 0.995
NOTE- If any component doesn't work, current will not pass through it.
A. 0.54
B. 0.75
C. 0.8
D. 0.93
E. 0.995
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01 Aug 2020, 07:08
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If I understand the question correctly, the circuit works as long as there's some functioning path from X to Y.
The path along the top will work as long as both A and B work. The probability they both work is (0.9)(0.8) = 0.72 = 18/25
The path along the bottom will work as long as C works, so the probability that path works is 0.75 = 3/4
So the circuit only fails if the top path and bottom path both fail, which will happen (7/25)(1/4) = 7/100 of the time. The remaining 93/100 of the time, the circuit works, so 0.93 is the answer.
I'd add, with these answer choices, it seems easy to estimate the answer without doing any calculation. The answer clearly must exceed 0.75, because that's the probability that the bottom path alone works, and it must exceed 0.75 by a fair amount, because path A is quite likely to work too. But the chance the circuit fails will be quite a bit larger than 0.005%, so E is too big, and D seems like the only plausible answer.
The path along the top will work as long as both A and B work. The probability they both work is (0.9)(0.8) = 0.72 = 18/25
The path along the bottom will work as long as C works, so the probability that path works is 0.75 = 3/4
So the circuit only fails if the top path and bottom path both fail, which will happen (7/25)(1/4) = 7/100 of the time. The remaining 93/100 of the time, the circuit works, so 0.93 is the answer.
I'd add, with these answer choices, it seems easy to estimate the answer without doing any calculation. The answer clearly must exceed 0.75, because that's the probability that the bottom path alone works, and it must exceed 0.75 by a fair amount, because path A is quite likely to work too. But the chance the circuit fails will be quite a bit larger than 0.005%, so E is too big, and D seems like the only plausible answer.
01 Aug 2020, 07:25
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nick1816
The electrical apparatus works as long as current can flow from left to right (from point X to Y). The three components A, B and C are independent. The probability that component A works is 0.8; the probability that component B works is 0.9; and the probability that component C works is 0.75. Find the probability that apparatus(shown below) will work ?
NOTE- If any component doesn't work, current will not pass through it.
A. 0.54
B. 0.75
C. 0.8
D. 0.93
E. 0.995
\(P_C\)*\(P_A\)*\(P_B\) + \(P_C\)*\(P_B\)*\(P_A\) + \(P_C\)*\(P_A\)*\(P_B\) + \(P_C\)*\(P_A\)*\(P_B\) + \(P_C\)*\(P_A\)*\(P_B\) NOTE- If any component doesn't work, current will not pass through it.
A. 0.54
B. 0.75
C. 0.8
D. 0.93
E. 0.995
= 0.06 + 0.135 + 0.015 + 0.54 + 0.18
= 0.93
OR
Estimating
\(P_C\)*\(P_A\)*\(P_B\)
= 0.005
But circuit will also not work for
\(P_C\)*\(P_A\)*\(P_B\) AND
\(P_C\)*\(P_A\)*\(P_B\) AND
So, failure > 0.005.
Thus E is eliminated.
Since each is independent. Success > 0.75(\(P_C\)) as \(P_A*P_B\) has to be added which is more than 0.05.
Hence C is also eliminated.
Answer D
