Problem 43575. Probabilities - More brains than luck

Created by Massimo Zanetti

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>This problem is related to</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains\"><w:r><w:t>Problem 596. More luck than brains</w:t></w:r></w:hyperlink><w:r><w:t> where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Using brain, the \"solver\" would be interested in computing the probability of passing a general test (with some other interesting probabilities) where the suite checks C times if the outcome of the solution is a random number between 1 and N.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>So, here is the problem:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>Each test in the suite checks if a random number between 1 and N is guessed.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>There are C tests in the suite.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Output these values, given inputs N,C,K:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>P = the probability of passing the test suite.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"2\"/></w:numPr></w:pPr><w:r><w:t>M = the mean number of times the function must be run to get a success.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>You will see that, for N=6 and C=3, then M=216.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

This problem is related to <a href = "http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains">Problem 596. More luck than brains</a>
where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.Using brain, the "solver" would be interested in computing the probability of passing a general test (with some other interesting probabilities) where the suite checks C times if the outcome of the solution is a random number between 1 and N.So, here is the problem:<ol><li>Each test in the suite checks if a random number between 1 and N is guessed.</li><li>There are C tests in the suite.</li></ol>Output these values, given inputs N,C,K:<ol><li>P = the probability of passing the test suite.</li><li>XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.</li><li>M = the mean number of times the function must be run to get a success.</li></ol>You will see that, for N=6 and C=3, then M=216.

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Last Solution submitted on Aug 18, 2020

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Problem 43575. Probabilities - More brains than luck

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Problem 43575. Probabilities - More brains than luck

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