(42S/DM42/Free42/Plus42) Birthday Probability Function

[Thomas Klemm]

It's less of an approximation but uses the formula:

\(
\begin{aligned}
\bar{p}(k)=\frac{_{365}P_{k}}{365^{k}}
\end{aligned}
\)

where \(_{n}P_{k}\) denotes permutation.

What I meant by "small values" is that with the HP-42S we can't go beyond \(k=195\) or we get the error: Out of Range
However, it still works with Free42 due to its extended range.

For an approximation we can use:

\(
\begin{aligned}
\bar{p}(n,k)
&\approx e^{-\frac{k(k-1)}{2n}} \\
&\approx \left(1 - \frac{k}{2n}\right)^{k-1} \\
\end{aligned}
\)

Here we assume that \(k \ll n\).

Example

40 ENTER
39 *
2 /
365 /
CHS
e^x

0.11801


1 ENTER
40 ENTER
2 /
365 /
-
39
y^x

0.11105