Suggest suitable sample spaces and identify the subset corre

Suggest suitable sample spaces, and identify the subset corresponding to the event A, for the following situation:

A money value x is chosen at random from the nancial pages of a newspaper; A is the event that the first digit of x is 1. Assume that all digits are possible as the firrst digit.

In each case discuss what the probability P(A) might be, commenting on how precise you can be, and on any assumptions you need to make

Solution

As the distirbution for the first digit of a number is approximately uniform, then the probability of 1 being the first digit is

P(A) = 1/10 = 0.1, as there are 10 possible digits.

This is true only if the distribution of the first digit is uniform. Having uniform distirbution is the assumption.

However, this may not be as precise if we are looking at \"top tens\", say, top 10 richest men in the world.

In there, you could possibly see number very close to each other, and not normally distirbuted, as they try to compete. In that case, our assumption may not hold. The statements above are only valid when the distribution of the first digit is uniform.