Determine the probability p that at least three models match the profile. ( Poisson scheme )
Suppose that four new computer models M1, M2, M3, M4 are being tested for
their reliability. The probability that a model satisfy the latest market standards are
p1 = 0.8 for model M1, p1 = 0.7 for model M2, p3 = 0.9 for model M3 and p4 = 0.6 for
model M4. Determine the probability p that at least three models match the profile.
I know I have to use the poisson's urn scheme and apply the formula for
$P(x geq 3)$ but I am at a loss on how to find the expected value in order to apply the formula so a little help would be appreciated.
probability
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
add a comment |
Suppose that four new computer models M1, M2, M3, M4 are being tested for
their reliability. The probability that a model satisfy the latest market standards are
p1 = 0.8 for model M1, p1 = 0.7 for model M2, p3 = 0.9 for model M3 and p4 = 0.6 for
model M4. Determine the probability p that at least three models match the profile.
I know I have to use the poisson's urn scheme and apply the formula for
$P(x geq 3)$ but I am at a loss on how to find the expected value in order to apply the formula so a little help would be appreciated.
probability
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
add a comment |
Suppose that four new computer models M1, M2, M3, M4 are being tested for
their reliability. The probability that a model satisfy the latest market standards are
p1 = 0.8 for model M1, p1 = 0.7 for model M2, p3 = 0.9 for model M3 and p4 = 0.6 for
model M4. Determine the probability p that at least three models match the profile.
I know I have to use the poisson's urn scheme and apply the formula for
$P(x geq 3)$ but I am at a loss on how to find the expected value in order to apply the formula so a little help would be appreciated.
probability
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
Suppose that four new computer models M1, M2, M3, M4 are being tested for
their reliability. The probability that a model satisfy the latest market standards are
p1 = 0.8 for model M1, p1 = 0.7 for model M2, p3 = 0.9 for model M3 and p4 = 0.6 for
model M4. Determine the probability p that at least three models match the profile.
I know I have to use the poisson's urn scheme and apply the formula for
$P(x geq 3)$ but I am at a loss on how to find the expected value in order to apply the formula so a little help would be appreciated.
probability
probability
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
asked Jan 4 at 8:09
The VirtuosoThe Virtuoso
407
407
add a comment |
add a comment |
1 Answer
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There are 5 ways this can happen. They all match the profile, or only one misses, either M1, M2, M3, or M4, and the other three match. So you sum up these 5 probabilities.
The probabilities of these 5 chances are $p_1p_2p_3p_4$, $(1-p_1)p_2p_3p_4$, $p_1(1-p_2)p_3p_4$, $p_1p_2(1-p_3)p_4$, and $p_1p_2p_3(1-p_4)$, respectively. Summing these up with the given $p$ values gives $0.3024+0.0756+0.1296+0.0336+0.2016=0.7428$
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
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1 Answer
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There are 5 ways this can happen. They all match the profile, or only one misses, either M1, M2, M3, or M4, and the other three match. So you sum up these 5 probabilities.
The probabilities of these 5 chances are $p_1p_2p_3p_4$, $(1-p_1)p_2p_3p_4$, $p_1(1-p_2)p_3p_4$, $p_1p_2(1-p_3)p_4$, and $p_1p_2p_3(1-p_4)$, respectively. Summing these up with the given $p$ values gives $0.3024+0.0756+0.1296+0.0336+0.2016=0.7428$
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson 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 |
There are 5 ways this can happen. They all match the profile, or only one misses, either M1, M2, M3, or M4, and the other three match. So you sum up these 5 probabilities.
The probabilities of these 5 chances are $p_1p_2p_3p_4$, $(1-p_1)p_2p_3p_4$, $p_1(1-p_2)p_3p_4$, $p_1p_2(1-p_3)p_4$, and $p_1p_2p_3(1-p_4)$, respectively. Summing these up with the given $p$ values gives $0.3024+0.0756+0.1296+0.0336+0.2016=0.7428$
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson 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 |
There are 5 ways this can happen. They all match the profile, or only one misses, either M1, M2, M3, or M4, and the other three match. So you sum up these 5 probabilities.
The probabilities of these 5 chances are $p_1p_2p_3p_4$, $(1-p_1)p_2p_3p_4$, $p_1(1-p_2)p_3p_4$, $p_1p_2(1-p_3)p_4$, and $p_1p_2p_3(1-p_4)$, respectively. Summing these up with the given $p$ values gives $0.3024+0.0756+0.1296+0.0336+0.2016=0.7428$
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
There are 5 ways this can happen. They all match the profile, or only one misses, either M1, M2, M3, or M4, and the other three match. So you sum up these 5 probabilities.
The probabilities of these 5 chances are $p_1p_2p_3p_4$, $(1-p_1)p_2p_3p_4$, $p_1(1-p_2)p_3p_4$, $p_1p_2(1-p_3)p_4$, and $p_1p_2p_3(1-p_4)$, respectively. Summing these up with the given $p$ values gives $0.3024+0.0756+0.1296+0.0336+0.2016=0.7428$
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
answered Jan 4 at 8:55
Erik ParkinsonErik Parkinson
9159
9159
New contributor
Erik Parkinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
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