---
title: "Birthday"
id: 57637
type: "computer_media"
slug: "october-1983-loader"
url: "http://localhost/computer_media/october-1983-loader/"
markdown_url: "http://localhost/computer_media/october-1983-loader.md"
published_at: "2024-10-06T01:07:18+00:00"
modified_at: "2026-03-30T21:16:43+00:00"
author: "David Anderson"
featured_image:
  url: "http://localhost/wp-content/uploads/2024/10/birthday-calc.png"
excerpt: "A compact Birthday Problem solver that streams 60 probability values, revealing exactly when shared birthdays become more likely than not."
category:
  - name: "Archived Media"
    slug: "archived-media"
    taxonomy: "category"
    url: "http://localhost/category/archived-media/"
post_tag:
  - name: "Downloadable"
    slug: "downloadable"
    taxonomy: "post_tag"
    url: "http://localhost/tag/downloadable/"
  - name: "TS 1000"
    slug: "ts1000"
    taxonomy: "post_tag"
    url: "http://localhost/tag/ts1000/"
model:
  - name: "Timex/Sinclair 1000"
    slug: "ts-1000"
    taxonomy: "model"
    url: "http://localhost/model/ts-1000/"
indiv:
  - name: "Gene G. Buza"
    slug: "gene-g-buza"
    taxonomy: "indiv"
    url: "http://localhost/indiv/gene-g-buza/"
genre:
  - name: "Entertainment"
    slug: "entertainment"
    taxonomy: "genre"
    url: "http://localhost/type/entertainment/"
media_contents:
  - id: 56727
    title: "Synchro-Sette October 1982"
    type: "computer_media"
    url: "http://localhost/computer_media/synchro-sette-october-1982/"
media_type: "Program"
programmers:
  - name: "Gene G. Buza"
    slug: "gene-g-buza"
    taxonomy: "indiv"
    url: "http://localhost/indiv/gene-g-buza/"
mediadate: "October 1982"
images:
  - url: "http://localhost/wp-content/uploads/2024/10/birthday-calc.png"
media_type_tags: "Entertainment, Software"
---

# Birthday

This program calculates the “Birthday Problem” probabilities, determining how many people are needed in a group before there is at least a 50% chance that two or more share the same birthday. It iterates from 1 to 60 people, printing each group size alongside the running probability that at least two share a birthday. The probability complement is computed iteratively: Q accumulates the product of (365−N)/365 terms, representing the chance that all birthdays are distinct, and then (Q−1)×−100 converts this to a percentage chance of a collision. The SCROLL command is used to prevent the display from pausing, allowing all 60 results to stream continuously past.

***

## Program Analysis

### Program Structure

The program is a straightforward iterative calculation across six lines. It initialises a probability accumulator, loops from 1 to 60, and prints results continuously using `SCROLL` to avoid the display filling up.

| Line | Purpose |
| --- | --- |
| `10` | Prints a multi-line description of the problem |
| `20` | Initialises `Q` to 1 (the probability all birthdays are unique, starting condition) |
| `30` | Opens the main loop, `N` = group size from 1 to 60 |
| `40` | `SCROLL` prevents the display from pausing between lines |
| `50` | Prints `N` and the collision probability as a percentage |
| `60` | Updates `Q` by multiplying in the next distinct-birthday factor |
| `70` | Closes the loop |

### Mathematical Approach

The Birthday Problem is solved using the complementary probability. `Q` holds the probability that all `N` people have distinct birthdays, computed as the running product:

`Q = (365/365) × (364/365) × (363/365) × … × ((365−N+1)/365)`

At each step, line `50` prints `-(100*(Q-1))`, which is equivalent to `100*(1-Q)` — converting the complement probability into a percentage chance that at least two people share a birthday. The negation trick avoids the need for a separate subtraction from 1, since `Q−1` is always negative or zero.

The classic result — that a group of 23 people suffices for a greater than 50% collision probability — will be clearly visible in the output around `N=23`.

### Key BASIC Idioms

- `SCROLL` at line `40` suppresses the scroll prompt, allowing all 60 lines of output to flow without user intervention.
- The use of commas in the `PRINT` statement at line `10` advances to successive print zones, indenting the title text.
- The expression `-(100*(Q-1))` is a compact idiom for `100*(1-Q)`, exploiting unary negation rather than rewriting the subtraction.
- `Q` is updated in place each iteration rather than recomputed from scratch, making this an efficient incremental calculation.

### Notable Techniques

The iterative update of `Q` at line `60` — multiplying by `(365-N)/365` — means the program never needs to compute a factorial or large product from scratch, keeping numerical operations within manageable floating-point range for all 60 iterations.

### Bugs and Anomalies

The loop begins at `N=1`, for which the collision probability is 0% (one person cannot share a birthday with anyone else). This is mathematically correct but slightly redundant as a starting point. The loop runs to `N=60`, well past the point (~23) where probability exceeds 50%, which is useful for demonstrating how quickly the probability approaches certainty near `N=60` (approximately 99.4%).

The title string on line `10` is not line-wrapped with explicit formatting — the text runs on as a single long string and relies on the display’s automatic wrapping, which may produce ragged output depending on screen width.

## Source Code

```
  10 PRINT ,,"PROGRAM TO DETERMINE THE NUMBER OF PEOPLE NEEDED TO HAVE AT     LEAST 50 PERCENT PROBABILITY OF HAVING TWO OR MORE WITH THE SAMEBIRTHDAY."
  20 LET Q=1
  30 FOR N=1 TO 60
  40 SCROLL 
  50 PRINT N,-(100*(Q-1))
  60 LET Q=Q*(365-N)/365
  70 NEXT N
```