Please explain how you solved it. It must be done without using software please,
ID: 3295490 • Letter: P
Question
Please explain how you solved it. It must be done without using software please, thank you.
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: The probability that a randomly selected person in a typical local bar environment is born within 25 miles of Manchester is 1/20 and: The chance that a person born within 25 miles of Manchester actually supports United is 7/10: The chance that a person born within 25 miles of Manchester actually supports United is 1/10;Explanation / Answer
Substitute the given values in the following Bayes theorem formula.
P(born within 25 miles of Manchester|support Manchester United)=P(born within 25 miles of Manchester)P(support Mancheter united|born within 25 miles of Manchester united)/{P(born within 25 miles of Manchester)P(support Mancheter united|born within 25 miles of Manchester united)+P(did not born within 25 miles of Mancheter united)P(did not support Manchester united|born within 25 miles of Manchester united)}
=(1/20*1/10)/{(1/20*1/10+19/20*7/10)} [assume, the chance that a person born within 25 miles of Manchester didnot actually support United is 7/10]
=0.0075