Problem 43575. Probabilities - More brains than luck

Created by Massimo Zanetti

Solve Later

{"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.

Solve

Solution Stats

58 Solutions
13 Solvers

Last Solution submitted on Dec 26, 2020

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Problem Tags

probabilities random guess test suite

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 43575. Probabilities - More brains than luck

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Suggested Problems

More from this Author14

Problem Tags

Community Treasure Hunt

Problem 43575. Probabilities - More brains than luck

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers13

Suggested Problems

More from this Author14

Problem Tags

Community Treasure Hunt

Players