Fibonacci Distribution

TL;DR

• A probability distribution constructed from the Fibonacci sequence, where Fibonacci numbers are used to represent event probabilities.
• Applied in examples to compute coin outcomes and lottery-number probabilities using specified initial values.
• Presented as a simple method for assigning probabilities, relying on the well-known Fibonacci sequence.

Definition

The Fibonacci distribution is a probability distribution based on the Fibonacci sequence. The Fibonacci sequence starts with 0 and 1, and each subsequent number is the sum of the previous two numbers (for example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on). In this distribution, each number in the Fibonacci sequence represents a probability of an event occurring.

Explanation

The distribution uses the Fibonacci sequence to determine probabilities for events by treating specific Fibonacci numbers as the probabilities of particular outcomes. The source describes using initial probabilities (for example, 0 and 1) for two outcomes and then applying the Fibonacci sequence to assign probabilities to other outcomes. The presentation frames the approach as a simple and easy way to calculate probabilities because it is founded on a widely known mathematical sequence.

Examples

Coin example

• Consider a coin with two outcomes: heads and tails.
• If the probability of the coin landing on heads is 0, and the probability of the coin landing on tails is 1, the Fibonacci distribution can be used to calculate the probabilities of heads and tails.
• Using the Fibonacci sequence, the probability of the coin landing on heads is 0.5, and the probability of the coin landing on tails is 0.5. This yields equal probability for heads and tails.

Lottery example

• Consider a lottery with 50 numbers where we want the probability of a certain number being drawn.
• If the probability of the number 1 being drawn is 0, and the probability of the number 2 being drawn is 1, the Fibonacci sequence is used to compute probabilities for the other numbers.
• Using the Fibonacci sequence, the probability of the number 3 being drawn is 0.5, the probability of the number 4 being drawn is 0.5, and so on. This implies each number has an equal probability of being drawn in the lottery.

Use cases

• The source states the Fibonacci distribution can be used to calculate the probability of events such as coin outcomes or the probability of a certain number being drawn in a lottery.
• It is described as useful because it provides a simple and easy way to calculate probabilities and is based on a well-known mathematical sequence.

Related terms

• Fibonacci sequence