Created
August 3, 2015 19:55
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Calculate the birthday problem distribution
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| <?php | |
| /** | |
| * Calculate chances for the birthday problem. | |
| */ | |
| $number_rolls = 100; | |
| // number of birthdays | |
| for ($i = 2; $i <= 100; ++$i) { | |
| $same_birthdays = 0; | |
| for ($j = 0; $j < $number_rolls; ++$j) { | |
| $numbers = []; | |
| $counter = $i; | |
| // distribute the birthdays | |
| while ($counter--) { | |
| $numbers[] = rand(1, 365); | |
| } | |
| // find the doubles | |
| $doubles = array_filter(array_count_values($numbers), function($value) { | |
| return $value != 1; | |
| }); | |
| if (count($doubles)) { | |
| ++$same_birthdays; | |
| } | |
| } | |
| print('For #' . $i . ' birthdays: ' . ($same_birthdays / $number_rolls * 100) . '%' . PHP_EOL); | |
| } |
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| For #2 birthdays: 0% | |
| For #3 birthdays: 1% | |
| For #4 birthdays: 2% | |
| For #5 birthdays: 4% | |
| For #6 birthdays: 6% | |
| For #7 birthdays: 6% | |
| For #8 birthdays: 4% | |
| For #9 birthdays: 10% | |
| For #10 birthdays: 6% | |
| For #11 birthdays: 20% | |
| For #12 birthdays: 10% | |
| For #13 birthdays: 25% | |
| For #14 birthdays: 24% | |
| For #15 birthdays: 24% | |
| For #16 birthdays: 27% | |
| For #17 birthdays: 38% | |
| For #18 birthdays: 34% | |
| For #19 birthdays: 35% | |
| For #20 birthdays: 49% | |
| For #21 birthdays: 49% | |
| For #22 birthdays: 47% | |
| For #23 birthdays: 49% | |
| For #24 birthdays: 55% | |
| For #25 birthdays: 59% | |
| For #26 birthdays: 60% | |
| For #27 birthdays: 55% | |
| For #28 birthdays: 65% | |
| For #29 birthdays: 64% | |
| For #30 birthdays: 74% | |
| For #31 birthdays: 72% | |
| For #32 birthdays: 77% | |
| For #33 birthdays: 82% | |
| For #34 birthdays: 80% | |
| For #35 birthdays: 77% | |
| For #36 birthdays: 83% | |
| For #37 birthdays: 87% | |
| For #38 birthdays: 83% | |
| For #39 birthdays: 89% | |
| For #40 birthdays: 93% | |
| For #41 birthdays: 84% | |
| For #42 birthdays: 92% | |
| For #43 birthdays: 92% | |
| For #44 birthdays: 99% | |
| For #45 birthdays: 94% | |
| For #46 birthdays: 91% | |
| For #47 birthdays: 98% | |
| For #48 birthdays: 95% | |
| For #49 birthdays: 96% | |
| For #50 birthdays: 98% | |
| For #51 birthdays: 98% | |
| For #52 birthdays: 97% | |
| For #53 birthdays: 98% | |
| For #54 birthdays: 98% | |
| For #55 birthdays: 100% | |
| For #56 birthdays: 99% | |
| For #57 birthdays: 100% | |
| For #58 birthdays: 100% | |
| For #59 birthdays: 100% | |
| For #60 birthdays: 99% | |
| For #61 birthdays: 100% | |
| For #62 birthdays: 99% | |
| For #63 birthdays: 100% | |
| For #64 birthdays: 100% | |
| For #65 birthdays: 99% | |
| For #66 birthdays: 100% | |
| For #67 birthdays: 100% | |
| For #68 birthdays: 100% | |
| For #69 birthdays: 100% | |
| For #70 birthdays: 100% | |
| For #71 birthdays: 100% | |
| For #72 birthdays: 100% | |
| For #73 birthdays: 100% | |
| For #74 birthdays: 100% | |
| For #75 birthdays: 100% | |
| For #76 birthdays: 100% | |
| For #77 birthdays: 100% | |
| For #78 birthdays: 100% | |
| For #79 birthdays: 100% | |
| For #80 birthdays: 100% | |
| For #81 birthdays: 100% | |
| For #82 birthdays: 100% | |
| For #83 birthdays: 100% | |
| For #84 birthdays: 100% | |
| For #85 birthdays: 100% | |
| For #86 birthdays: 100% | |
| For #87 birthdays: 100% | |
| For #88 birthdays: 100% | |
| For #89 birthdays: 100% | |
| For #90 birthdays: 100% | |
| For #91 birthdays: 100% | |
| For #92 birthdays: 100% | |
| For #93 birthdays: 100% | |
| For #94 birthdays: 100% | |
| For #95 birthdays: 100% | |
| For #96 birthdays: 100% | |
| For #97 birthdays: 100% | |
| For #98 birthdays: 100% | |
| For #99 birthdays: 100% | |
| For #100 birthdays: 100% |
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