Question

English and American spellings are rigour and rigor, 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

Answer 1

Pr(Vowel n Englishman) = (1/2) * (40/100) = (0.5)*(0.4) = 0.2

Explanation:

By conditional probability,

Pr(A|B) = Pr(A n B)/ Pr(B) and it can be written as:

Pr(A n B) = Pr(A|B) * Pr(B).

The question wants us to compute the probability that a vowel is picked and it is written by an Englishman. Going by conditional probability, we have that:

Pr(Vowel | Englishman) = Pr(Vowel n Englishman)/Pr(Englishman),

and this is;

Pr(Vowel n Englishman) = Pr(Vowel | Englishman) * Pr(Englishman)

Recall that the word is ==> RIGOUR for Englishman, and it has 3 vowels. The total number of alphabet of the words is 6.

Therefore,

Pr(Vowel | Englishman) = (3/6) = 1/2 = 0.5

Pr(Englishman) = 40/100 = 0.4.

Following the conditional probability formula, Pr(Vowel n Englishman) = Pr(Vowel | Englishman) * Pr(Englishman),

Pr(Vowel n Englishman) = (0.5 * 0.4) = 0.2