{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2025-12-14T01:33:56.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2025-12-14T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":43575,"title":"Probabilities - More brains than luck","description":"This problem is related to \u003chttp://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains Problem 596. More luck than brains\u003e\r\nwhere the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6. \r\n\r\nUsing 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.\r\n\r\nSo, here is the problem:\r\n\r\n# Each test in the suite checks if a random number between 1 and N is guessed. \r\n# There are C tests in the suite.\r\n\r\nOutput these values, given inputs N,C,K:\r\n\r\n# P = the probability of passing the test suite.\r\n# XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\r\n# M = the mean number of times the function must be run to get a success.\r\n\r\nYou will see that, for N=6 and C=3, then M=216. ","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains\"\u003eProblem 596. More luck than brains\u003c/a\u003e\r\nwhere the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.\u003c/p\u003e\u003cp\u003eUsing 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.\u003c/p\u003e\u003cp\u003eSo, here is the problem:\u003c/p\u003e\u003col\u003e\u003cli\u003eEach test in the suite checks if a random number between 1 and N is guessed.\u003c/li\u003e\u003cli\u003eThere are C tests in the suite.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eOutput these values, given inputs N,C,K:\u003c/p\u003e\u003col\u003e\u003cli\u003eP = the probability of passing the test suite.\u003c/li\u003e\u003cli\u003eXK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\u003c/li\u003e\u003cli\u003eM = the mean number of times the function must be run to get a success.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eYou will see that, for N=6 and C=3, then M=216.\u003c/p\u003e","function_template":"function [P,XK,M] = test_suite_prob(N,C,K)\r\n  P=1;\r\n  XK=K;\r\n  M=1;\r\nend","test_suite":"%%\r\nC=1; N=6; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.166666; XKc=0.138888; Mc=6;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=3; N=6; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.004629; XKc=0.004608; Mc=216;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=2; N=6; K=6;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.027777; XKc=0.024128; Mc=36;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=8; N=2; K=20;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.003906; XKc=0.003626; Mc=256;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=4; N=5; K=7;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.001600; XKc=0.001584; Mc=625;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=5; N=1; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=1; XKc=0; Mc=1;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":85738,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-18T15:58:33.000Z","updated_at":"2025-11-21T18:42:36.000Z","published_at":"2016-10-18T15:58:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 596. More luck than brains\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, here is the problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach test in the suite checks if a random number between 1 and N is guessed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are C tests in the suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput these values, given inputs N,C,K:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = the probability of passing the test suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eXK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM = the mean number of times the function must be run to get a success.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will see that, for N=6 and C=3, then M=216.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":43575,"title":"Probabilities - More brains than luck","description":"This problem is related to \u003chttp://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains Problem 596. More luck than brains\u003e\r\nwhere the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6. \r\n\r\nUsing 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.\r\n\r\nSo, here is the problem:\r\n\r\n# Each test in the suite checks if a random number between 1 and N is guessed. \r\n# There are C tests in the suite.\r\n\r\nOutput these values, given inputs N,C,K:\r\n\r\n# P = the probability of passing the test suite.\r\n# XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\r\n# M = the mean number of times the function must be run to get a success.\r\n\r\nYou will see that, for N=6 and C=3, then M=216. ","description_html":"\u003cp\u003eThis problem is related to \u003ca href = \"http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains\"\u003eProblem 596. More luck than brains\u003c/a\u003e\r\nwhere the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.\u003c/p\u003e\u003cp\u003eUsing 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.\u003c/p\u003e\u003cp\u003eSo, here is the problem:\u003c/p\u003e\u003col\u003e\u003cli\u003eEach test in the suite checks if a random number between 1 and N is guessed.\u003c/li\u003e\u003cli\u003eThere are C tests in the suite.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eOutput these values, given inputs N,C,K:\u003c/p\u003e\u003col\u003e\u003cli\u003eP = the probability of passing the test suite.\u003c/li\u003e\u003cli\u003eXK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\u003c/li\u003e\u003cli\u003eM = the mean number of times the function must be run to get a success.\u003c/li\u003e\u003c/ol\u003e\u003cp\u003eYou will see that, for N=6 and C=3, then M=216.\u003c/p\u003e","function_template":"function [P,XK,M] = test_suite_prob(N,C,K)\r\n  P=1;\r\n  XK=K;\r\n  M=1;\r\nend","test_suite":"%%\r\nC=1; N=6; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.166666; XKc=0.138888; Mc=6;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=3; N=6; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.004629; XKc=0.004608; Mc=216;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=2; N=6; K=6;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.027777; XKc=0.024128; Mc=36;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=8; N=2; K=20;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.003906; XKc=0.003626; Mc=256;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=4; N=5; K=7;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=0.001600; XKc=0.001584; Mc=625;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );\r\n%%\r\nC=5; N=1; K=2;\r\n[P,XK,M] = test_suite_prob(N,C,K);\r\nPc=1; XKc=0; Mc=1;\r\ntol=1e-6;\r\nassert( (abs(P-Pc)\u003ctol)\u0026(abs(XK-XKc)\u003ctol)\u0026(abs(M-Mc)\u003ctol) );","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":85738,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":19,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2016-10-18T15:58:33.000Z","updated_at":"2025-11-21T18:42:36.000Z","published_at":"2016-10-18T15:58:33.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"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\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThis problem is related to\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"http://it.mathworks.com/matlabcentral/cody/problems/596-more-luck-than-brains\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eProblem 596. More luck than brains\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing 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.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eSo, here is the problem:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eEach test in the suite checks if a random number between 1 and N is guessed.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThere are C tests in the suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput these values, given inputs N,C,K:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eP = the probability of passing the test suite.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eXK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"ListParagraph\\\"/\u003e\u003cw:numPr\u003e\u003cw:numId w:val=\\\"2\\\"/\u003e\u003c/w:numPr\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eM = the mean number of times the function must be run to get a success.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYou will see that, for N=6 and C=3, then 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