Respuesta :
Answer:
20% conditional probability that I am not working, if I am at my office
Step-by-step explanation:
Conditional probability formula:
[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: Being at the office.
Event B: Not working.
I am at my office AND not working 2% of the time.
This means that [tex]P(A \cap B) = 0.02[/tex]
I am at my office 10% of the time.
This means that [tex]P(A) = 0.1[/tex]
What is the conditional probability that I am not working, if I am at my office?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(B|A) = \frac{0.02}{0.1}[/tex]
[tex]P(B|A) = 0.2[/tex]
20% conditional probability that I am not working, if I am at my office
