How would we express the relative probability given odds ratios in this problem?

Question

Hypothetical scenario:

Given: In a population, we know there are 3 people who have a car for every 5 people who have a scooter. There are also people who have a bicycle; but we do not know about them.

Also given: In a subset of that population, we find there are 5 people who have a car for every 3 people who have a scooter. There are also people who have a bicycle; but we do not know about them.

Conditions: We know only the above two ratios - ie, 3 cars : 5 scooters for the population; and 5 cars : 3 scooters for the subset. We do not know total population or total subset. By extension, we do not know how many people have bicycles either in the population or in the subset. Assume that cars plus scooters plus bicycles equals total population.

Problem: How might we represent or express the probability of a person in this population having a car?

Thank you in advance for not just any answer (if an answer is possible) but also reasoning.

VD.

Answer 1

Probability = (number of successes) / (number of observations)

Probability is a number between 0 (never) and 1 (always). It may also be expressed as a fraction (between 0 and 1) or a percent (between 0% and 100%).

For the entire population:

%cars + %scooters + %bicycles = 100%

The cardinal values in the sample may be obtained from any large population; they are not helpful.

However, the actual ratios of percentages possible are:

%cars %scooters %bicycles

3% 5% ? %

6% 10% ? %

. . .

This sample does not represent the population. For enough observations, it remains possible, but not very probable (i.e., low probability of it happening -- e.g., selecting 10 people and getting 10 females).

The probability of a person having a car is one of: 3x%, where x = 1, 2, 3, ..., 18