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Sagot :
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
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