probability of a circuit operating
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Circuit
Hello. Please see the link for a diagram explaining the problem. I am new here so I upload a picture directly. Basically I have a circuit that with switches that close with probability p and open with probability (1-p). I would like to find the probability that the circuit is connected from left to the right.
I tried several different methods but they all have different results. Short of enumerating all 32 possibilities, I can't think of a smarter method to do this problem.
Here is my results:
Let $A_1 = P(A B closed)$, $A_2 = P(A E D closed)$, $A_3 = P(CD closed$, $A_4 = P(CEB closed)$.
Then
$$P(circuit works) = P( A_1 cup A_2cup A_3 cup A_4) = P(A_1) + P(A_2 - A_1) + P(A_3 - A_2 - A_1) + P(A_4 - A_3 - A_2 - A_1) $$
This works out to be
$$ P(circuit works) = 4p^5 - 9p^4 + 2p^3 + 4p^2$$
probability
asked Nov 20 at 10:19
Chen Ee Woon
6
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Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
-1
down vote
favorite
Circuit
Hello. Please see the link for a diagram explaining the problem. I am new here so I upload a picture directly. Basically I have a circuit that with switches that close with probability p and open with probability (1-p). I would like to find the probability that the circuit is connected from left to the right.
I tried several different methods but they all have different results. Short of enumerating all 32 possibilities, I can't think of a smarter method to do this problem.
Here is my results:
Let $A_1 = P(A B closed)$, $A_2 = P(A E D closed)$, $A_3 = P(CD closed$, $A_4 = P(CEB closed)$.
Then
$$P(circuit works) = P( A_1 cup A_2cup A_3 cup A_4) = P(A_1) + P(A_2 - A_1) + P(A_3 - A_2 - A_1) + P(A_4 - A_3 - A_2 - A_1) $$
This works out to be
$$ P(circuit works) = 4p^5 - 9p^4 + 2p^3 + 4p^2$$
probability
asked Nov 20 at 10:19
Chen Ee Woon
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Circuit
Hello. Please see the link for a diagram explaining the problem. I am new here so I upload a picture directly. Basically I have a circuit that with switches that close with probability p and open with probability (1-p). I would like to find the probability that the circuit is connected from left to the right.
I tried several different methods but they all have different results. Short of enumerating all 32 possibilities, I can't think of a smarter method to do this problem.
Here is my results:
Let $A_1 = P(A B closed)$, $A_2 = P(A E D closed)$, $A_3 = P(CD closed$, $A_4 = P(CEB closed)$.
Then
$$P(circuit works) = P( A_1 cup A_2cup A_3 cup A_4) = P(A_1) + P(A_2 - A_1) + P(A_3 - A_2 - A_1) + P(A_4 - A_3 - A_2 - A_1) $$
This works out to be
$$ P(circuit works) = 4p^5 - 9p^4 + 2p^3 + 4p^2$$
probability
asked Nov 20 at 10:19
Chen Ee Woon
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Circuit
Hello. Please see the link for a diagram explaining the problem. I am new here so I upload a picture directly. Basically I have a circuit that with switches that close with probability p and open with probability (1-p). I would like to find the probability that the circuit is connected from left to the right.
I tried several different methods but they all have different results. Short of enumerating all 32 possibilities, I can't think of a smarter method to do this problem.
Here is my results:
Let $A_1 = P(A B closed)$, $A_2 = P(A E D closed)$, $A_3 = P(CD closed$, $A_4 = P(CEB closed)$.
Then
$$P(circuit works) = P( A_1 cup A_2cup A_3 cup A_4) = P(A_1) + P(A_2 - A_1) + P(A_3 - A_2 - A_1) + P(A_4 - A_3 - A_2 - A_1) $$
This works out to be
$$ P(circuit works) = 4p^5 - 9p^4 + 2p^3 + 4p^2$$
probability
probability
asked Nov 20 at 10:19
Chen Ee Woon
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 10:19
Chen Ee Woon
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 10:19
Chen Ee Woon
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 10:19
Chen Ee Woon
6
asked Nov 20 at 10:19
Chen Ee Woon
6
6
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Chen Ee Woon is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
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Chen Ee Woon is a new contributor. Be nice, and check out our Code of Conduct.
Chen Ee Woon is a new contributor. Be nice, and check out our Code of Conduct.
Chen Ee Woon is a new contributor. Be nice, and check out our Code of Conduct.
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