Question

I am at my office AND not working 2\%2% of the time. I am at my office 10\%10% of the time. What is the conditional probability that I am not working, if I am at my office?

Answer 1

Answer:

20% conditional probability that I am not working, if I am at my office

Step-by-step explanation:

Conditional probability formula:

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ 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 $P(A \cap B) = 0.02$

I am at my office 10% of the time.

This means that $P(A) = 0.1$

What is the conditional probability that I am not working, if I am at my office?

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$P(B|A) = \frac{0.02}{0.1}$

$P(B|A) = 0.2$

20% conditional probability that I am not working, if I am at my office