Probability1

//REPLACEMENTS
function getList($A,$k) {
    $result = [];

    while (count($result) < $k) {
        $sum = 0;
        foreach ($A as $key => $value) {
            $sum += $value;
        }

        $rnd = rand(0,$sum * 100000) / 100000;

        $sum = 0;
        foreach ($A as $key => $value) {
            $sum += $value;
            if ($rnd <= $sum) {
                $result[] = $key;
                break;
            }
        }
    }
    return $result;
}

function getQi($A,$k) {
    foreach ($A as $key => $value) {
        $A[$key] = 1 - pow(1 - $value,1.0 / $k);
    }
    return $A;
}

//P_i percentages for list A. SUMS to 10 or in this case K
$list = [
    "A" => .25,
    "B" => .25,
    "C" => .25,
    "D" => .25,
    "E" => .65,
    "F" => .65,
    "G" => .25,
    "H" => .25,
    "I" => .52,
    "J" => .5,
    "K" => .25,
    "L" => .25,
    "M" => .25,
    "N" => .25,
    "O" => .25,
    "P" => .25,
    "Q" => .28,
    "R" => .3,
    "S" => .25,
    "T" => .25,
    "U" => .5,
    "V" => .5,
    "W" => .5,
    "X" => .5,
    "Y" => .7,
    "Z" => .9
];


//Occurrences list for keeping track
$occurences = [
    "A" => 0,
    "B" => 0,
    "C" => 0,
    "D" => 0,
    "E" => 0,
    "F" => 0,
    "G" => 0,
    "H" => 0,
    "I" => 0,
    "J" => 0,
    "K" => 0,
    "L" => 0,
    "M" => 0,
    "N" => 0,
    "O" => 0,
    "P" => 0,
    "Q" => 0,
    "R" => 0,
    "S" => 0,
    "T" => 0,
    "U" => 0,
    "V" => 0,
    "W" => 0,
    "X" => 0,
    "Y" => 0,
    "Z" => 0
];

//Algorithm
//First get the Q_i percentages
$probs = getQi($list,10);

//Do it 100,000 times
for ($i=0; $i < 100000; $i++) {
    //Generate the list using getList function Algorithm
    $result = getList($probs,10);

    //Go through each letter A to Z
    foreach ($occurences as $key => $value) {
        //If the Generated list $result contains the letter at least once, increment its occurrence variable
        if (in_array($key,$result))
            $occurences[$key] += 1;
    }
}

foreach ($occurences as $key => $value) {
    $occurences[$key] = $value / 1000;
}
printArray($occurences);
//Result of printing is
/*
Array
(
    [A] => 20.585
    [B] => 20.312
    [C] => 20.692
    [D] => 20.599
    [E] => 20.591
    [F] => 20.729
    [G] => 20.557
    [H] => 20.597
    [I] => 42.436
    [J] => 42.436
    [K] => 20.734
    [L] => 20.322
    [M] => 20.56
    [N] => 20.691
    [O] => 20.567
    [P] => 20.551
    [Q] => 23.119
    [R] => 24.879
    [S] => 20.81
    [T] => 20.605
    [U] => 42.478
    [V] => 42.379
    [W] => 42.774
    [X] => 42.765
    [Y] => 61.587
    [Z] => 83.658
)
*/