Question

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 percent of the English-speaking men at the hotel are English and 60 percent are Americans, what is the probability that the writer is an Englishman?

Answer 1

Answer:

The probability is 5/11

Step-by-step explanation:

Let's call V the event that the letter taken at random is a vowel.

Let's call E the event that the man is English and A to the event that the man is American.

If 40 percent of the English-speaking men at the hotel are English means P(E)=0.40 and 60 percent are Americans means P(A)=0.60

In ''color'' we have 2 vowels out of 5 letters so P(V/A)=2/5

In ''colour'' we have 3 vowels out of 6 letters so P(V/E)=3/6=1/2

P(E/V)=P(E∩ V)/P(V)

P(V)=P(V|E)P(E) +P(V|A)P(A)

P(V)=(1/2)0.40+(2/5)0.60=0.44

P(E∩V)=P(V|E)P(E)=(1/2)0.40=0.20

P(E/V)=0.20/0.44=0.45454545=5/11