Answer to Question #145636 in Statistics and Probability for qwerty

Question

4. 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 0.10, 0.08, and 0.12, respectively. The inspections by the three departments are sequential and independent.
Conditional Probability, Independence, Product Rule - Answers must be in DECIMAL form.

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

Answer 1

(a) We use the fact that departments are independent. We can use multiplication rule for independent events(see https://www.statisticshowto.com/multiplication-rule-probability/) and get: $p=(1-0.1)\cdot0.08=0.072$.

(b) Since the events are sequential, it means that the batch survived first and second department. Then, the probability is: $p=(1-0.1)\cdot(1-0.08)\cdot0.12=0.09936$

Answer: (a) 0.072, (b) 0.09936.