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13. (6 marks) While visiting a bookstore in London, you observe some people who is clearly a fan of J. K
Rowling (the author of Harry Potter series). What is the probability that they were actually born in
England? (Hint: apply the Beures' theorem). You may write the final result as a fraction.
Assume that:
1) The probability that a randomly selected person in a typical local bookstore environment is born in
England is 1/20;
2) The chance that a person born in England actually is a fan of J. K Rowling is 3/5;
3) The probability that a person not born in England and is a fan of J. K. Rowling is 1/10.

Respuesta :

Using conditional probability, it is found that there is a 0.24 = 24% probability that they were actually born in  England.

What is Conditional Probability?

  • Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

In this problem, the events are:

  • Event A: The person is a fan of J.K. Rowling.
  • Event B: The person was born in England.

The percentages associated with the person being a fan of J.K. Rowling are:

  • [tex]\frac{3}{5} = 0.6[/tex] of [tex]\frac{1}{20} = 0.05[/tex](born in England).
  • [tex]\frac{1}{10} = 0.1[/tex] of [tex]\frac{19}{20} = 0.95[/tex](not born in england).

Hence:

[tex]P(A) = 0.6(0.05) + 0.1(0.95) = 0.125[/tex]

The probability of both is:

[tex]P(A \cap B) = 0.6(0.05) = 0.03[/tex]

Hence, the conditional probability is:

[tex]P(B|A) = \frac{0.03}{0.125} = 0.24[/tex]

0.24 = 24% probability that they were actually born in  England.

To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287