Respuesta :
Answer:
12.22% probability that a person who confessed to a crime is guilty
Step-by-step explanation:
We use the conditional probability formula to solve this question. It 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 question, we have that:
Event A: Confessing
Event B: Being guilty
Probability of confessing:
10% of 97%(non-guilty) or 45% of 3%(guilty). So
[tex]P(A) = 0.1*0.97 + 0.45*0.03 = 0.1105[/tex]
Confessing and being guilty:
3% are guilty, and of those, 45% confess. So
[tex]P(A \cap B) = 0.03*0.45 = 0.0135[/tex]
What is the probability that a person who confessed to a crime is guilty?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0135}{0.1105} = 0.1222[/tex]
12.22% probability that a person who confessed to a crime is guilty
