# Batches of serum are processed by three different departments having rejection rates of 0.10, 0.08, and 0.12 respectively. What is the probability that a batch of serum survives the first departmental inspection but is rejected by the second department?

## What is the probability that a batch of serum is rejected by the third department?

May 1, 2018

1)The probability is 0.9xx0.08 = 0.072 = 7.2%
2) The probability is 0.9xx0.92xx0.12 = 0.09936 = 9.936%

#### Explanation:

The rejection rates of the three departments are 0.1, 0.08, and 0.12 respectively.

This means 0.9, 0.92 and 0.88 is the probability that the serum passes the test in each department separately.

The probability that the serum passes the first inspection is 0.9
The probability that it fails the second inspection is 0.08. Thus its conditional probability is 0.9xx0.08 = 0.072 = 7.2%

For the serum to be rejected by the third department, it must first pass the first and second inspections. The conditional probability of this is $0.9 \times 0.92$. The rejection rate of the third department is 0.12, so the complete probability of rejection by the third department is 0.9xx0.92xx0.12 = 0.09936 = 9.936%