Solve no 4 explain it; but be brief) Problem 3 (20 points) State the general for

Question

Solve no 4 explain it; but be brief) Problem 3 (20 points) State the general form of the pelusion-Exclusion Principle for n sets A,A Ani in terms of the cardinalities of the themselves; and thei ions. (the sets can have arbitrary and non-null intersections) Apply this principle to ind the number of integers between 881 and 6709 that are divisible by 2 or 3 or 5 or 7 Problem 420points) factories (A, B, C) where desk lamps are manufactured. A Quality Control Manager (QCM) is responsible or iny ogating the source of found defects. This is what the QCM knows about the company's desk lamp production and ible source of defects tory % of total production 0.35 P(A) 0.35 P(B) 0.30 P(C) Probability of defective lamps 0.015 P(D |A) 0.010 P(D |B) 0.020 P(D |C) The QCM would like to answer the following question: If a randomly selected lamp is defective that the lamp was manufactured in factory C?

Explanation / Answer

We will use the Baye's theorem to solve this, so for finding the probability that a lamp is found defective is from factory C, given by P(C/D), we have

P(C/D)= {P(D/C)P(C)}/{P(D/A)P(A)+P(D/B)P(B)+P(D/C)P(C)}

= {0.020*0.30}/{(0.015)(0.35)+(0.010)(0.35)+(0.020)(0.30)}

=0.4068=0.41 (approximately)

Thus a lamp found defective has a probability of 0.41 approximately to be from factory C.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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