Answer to Question #347834 in Statistics and Probability for Ali

Question

A manufacturer of a flu vaccine is concerned about the quality of its flu serum. Batches of serum are processed by three different departments having rejection rates of 0.20, 0.08, and 0.12, respectively. The inspections by the three departments are sequential and independent.

(a) What is the probability that a batch of serum survives the first two departmental inspection but is rejected by the third department?

(b) What is the probability that a batch of serum is rejected by the first department?

Answer 1

(a) We use the fact that departments are independent.

Since the events are sequential, it means that the batch survived the first and the second department. We can use multiplication rule for independent events and get

$$p=(1-0.20)(1-0.08)(0.12)=0.08832$$

(b)The probability is 

$$p=0.2$$