Hello, SydneyBristow!

Here's the first one . . .

This requires repeated use of Bayes' Theorem . . .1. English and American spellings are "colour" and "color", respectively.

A man staying at a Parisian hotel writes this word, and a letter taken

at random from his spelling is found to be a vowel.

If 40% of the English-speaking men at the hotel are English and 60% are Americans,

what is the probability that the writer is an Englishman?

We have: .

We want: .

From [1] we have: .

. .

From [2] we have: .

. .

Hence: .

Substitute [4] and [5] into [3]: .

. .