7: While watching a game of Champions League football in a cafe, you observe som

Question

7: While watching a game of Champions League football in a cafe, you observe someone who is clearly supporting Manchester United in the game. What is the probability that they were actually born within 25 miles of Manchester? Assume that: 1. The probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is 1/20 and; 2. The chance that a person born within 25 miles of Manchester actually supports United is 7/10; 3. The chance that a person born within 25 miles of Manchester actually supports United is 1/10

Explanation / Answer

I think your last statment must be "actually doesn't support", it must be a typo.

Here' the SOLUTION:

Define

• B - event that the person is born within 25 miles of Manchester

• C - event that the person supports United.

We want P(B|C).

By Bayes’ Theorem,

P(B|C) = P(C|B)P(B)/P(C)

= P(C|B)*P(B) / P(C|B)*P(B) + P(C|B' )*P(B' )

= (7/10* 1 /20) / (7 /10 *1/20 + 1/10 *19/20)

= 7/26

0.269.

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