A bike manufacturing factory has two plants P and Q. Plant P manufactures 60…
2021
A bike manufacturing factory has two plants P and Q. Plant P manufactures 60 percent of bikes and plant Q manufactures 40 percent. 80 percent of the bikes at plant P and 90 percent of the bikes at plant Q are rated of standard quality. A bike is chosen at random and is found to be of standard quality. What is the probability that it has come from plant P?
- A.
3/7
- B.
6/7
- C.
5/7
- D.
4/7
Attempted by 11 students.
Show answer & explanation
Correct answer: D
Define events: P = bike from Plant P, Q = bike from Plant Q, S = standard quality bike.
Given probabilities: P(P) = 0.6, P(Q) = 0.4.
Conditional probabilities: P(S|P) = 0.8, P(S|Q) = 0.9.
Total probability of standard quality bike: P(S) = (P(P) * P(S|P)) + (P(Q) * P(S|Q)) = (0.6 * 0.8) + (0.4 * 0.9) = 0.48 + 0.36 = 0.84.
Probability that it came from Plant P: P(P|S) = (P(P) * P(S|P)) / P(S) = 0.48 / 0.84 = 4 / 7.
Final Answer: Option 4 (4/7)