3. Solve below: 3a. A recording company obtains the blank CDs used to produce it

Question

3. Solve below:

3a.

A recording company obtains the blank CDs used to produce its labels from three compact disk manufacturers: I, II, and III. The quality control department of the company has determined that 7% of the compact disks produced by manufacturer I are defective, 5% of those produced by manufacturer II are defective, and 4% of those produced by manufacturer III are defective. Manufacturers I, II, and III supply 37%, 45%, and 18%, respectively, of the compact disks used by the company. What is the probability that a randomly selected label produced by the company will contain a defective compact disk?

a) 0.0259

b) 0.0072

c) 0.0556

d) 0.0225

e) 0.1600

f) None of the above.

3b.

Suppose that 11 green balls and 14 purple balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn?

a) 0.8800

b) 0.6000

c) 0.5600

d) 0.1276

e) 0.4400

f) None of the above.

Explanation / Answer

a) P(manufacture I) = 0.37

P(manufacture II) = 0.45

P(manufacture III) = 0.18

P(defective | manufacture I) = 0.07

P(defective | manufacture II) = 0.05

P(defective | manufacture III) = 0.04

P(defective) = P(defective | manufacture I) * P(manufacture I) + P(defective | manufacture II) * P(manufacture II) + P(defective | manufacture III) * P(manufacture III)

             = 0.07 * 0.37 + 0.05 * 0.45 + 0.04 * 0.18

             = 0.0556

Option-C)

b) P(second ball is purple ball) = 14/25 = 0.56

Option-C)

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

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