Respuesta :
Answer:
0.9 = 90% probability that the suspect actually committed the crime.
Step-by-step explanation:
Conditional Probability
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:
Event A: Charged
Event B: Committed the crime.
16% of crimes of this type end up in a criminal charge.
This means that [tex]P(A) = 0.16[/tex]
Probability of being charged and committing the crime:
90% of 16%, so:
[tex]P(A \cap B) = 0.9*0.16[/tex]
What is the chance that the suspect actually committed the crime?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.9*0.16}{0.16} = 0.9[/tex]
0.9 = 90% probability that the suspect actually committed the crime.
