A bike shop uses two manufacturing plants, one in region A and the other in regi

Question

A bike shop uses two manufacturing plants, one in region A and the other in region B, to build its bicycles. Four times as many bicycles are built in region B as in region A. The percentage of defective bikes from region B is three times that from region A. All bicycles are sent to a central warehouse, and one bicycle is chosen for inspection. If the bicycle is defective, find the probability that it came from region B. Let D be the event that the inspected bike is defective, A be the event that the inspected bike is from region A, and B be the event that the inspected bike is from region B. Find the probabilities of A and B and the version of Bayes Theorem that will be used in this situation. Type integers or simplified fractions.) The problem statement indicat P)d PB The formula needed to answer the question is P(BD) The problem statement indicates that P(A) and P(B)The formula needed to answer the question is P(BID) P(DIA). P(A)+P(DIB) P(B) P(DB) , P(B) O B. The probability that the chosen bicycle came from region B is Type an integer or a simplified fraction.)

Explanation / Answer

P(B) = 4 P(A)

P(A) + P(B) = 1

hence

P(A) = 1/ 5

P(B) = 4/5

P(B|D) = P(B and D) / P(D)

P(D|B) = 3 P(D|A)

hence

required probability = 4/5 * P(D|B) / (4/5 P(D|B) + 1/5 P(D|A))

= 4/5 * 3 /(4/5 *3 + 1/5 * 1)

= 0.923076

Please rate

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.