Question

Let Q denote the number of times a printer in a local library will run out of paper: 0, 1, 2, or 3 times in a given day. Let R denote the number of times the circulation desk clerk is called away from the desk. Their joint probability distribution is given in the “Joint Probability” worksheet labeled “Joint Probability” in the Excel file.

 

Find P(R = 2 | Q = 2). Give your answer to 3 decimal places.

Answer 1

$P(Q=2) =P(r=1,q=2)+P(r=2,q=2)+P(r=3,q=2) \\ =0.02+0.15+0.05=0.22$

Therefore

$P(R=2 |Q=2)=\frac{P(r=3,q=2)}{P(Q=2)} \\ =\frac{0.15}{0.22} \\ =0.682$