#-*-Mode: perl;-*-


eval "\$opt_$1=\$2" while $ARGV[0] =~ /^(\w+)=(.*)/ && shift;

$k = $opt_k;
$N = $opt_N;
$p = $opt_p;

print "N, number of possible events: $N\n";
print "k, number of events of the type we're interested in: $k\n";
print "p, probability of event type k: $p\n";

print "probability of getting exactly $k events: ", 
    &binomial($N, $k, $p), "\n";
print "probability of getting $k or more events: ", 
    &cumBinomial($N, $k, $p), "\n";

sub binomial {
    local($N, $k, $p) = @_;
    local($q) = 1 - $p;
    &binomCoeff($N, $k) * ($p ** $k) * ($q ** ($N - $k));
}

sub cumBinomial {
    local($N, $k, $p) = @_;
    local($sum) = &binomial($N, $k, $p);
    while ($k < $N) {
	$k++;
	$sum += &binomial($N, $k, $p);
    }
    $sum;
}

sub binomCoeff {
    local($N, $k) = @_;
    &fact($N) / (&fact($k) * &fact($N - $k));
}

sub fact {
    local($N) = @_;
    if (!$N) {return 1;}
    else {$N * &fact($N - 1);}
}