Question

A product is made up of three parts that act independently of each other. If any of the parts is defective, the product is defective. Part one is defective 5% of the time, part two is defective 10% of the time, and part three is defective 15% of the time. Find the probability of a defective product.

Answer 1

Answer: Probability of defective product is 0.00075.

Step-by-step explanation:

Since we have given that

Probability of getting defective in part one = 5%

Probability of getting defective in part two = 10%

Probability of getting defective in part three = 15%

Since they are independent of each other.

So, Probability of a defective product is given by

$P(One)\times P(Two)\times P(Three)\\\\=0.05\times 0.10\times 0.15\\\\=0.00075$

Hence, Probability of defective product is 0.00075.

Answer 2

Answer:

The probability that a product is defective is 0.2733.

Step-by-step explanation:

A product consists of 3 parts. If any one of the part is defective the whole product is considered as defective.

The probability of the 3 parts being defective are:

P (Part 1 is defective) = 0.05

P (part 2 is defective) = 0.10 P (part 3 is defective) = 0.15

Compute the probability that a product is defective as follows:

P (Defective product) = 1 - P (non-defective product)

= 1 - P (None of the 3 parts are defective)

= 1 - P (Part 1 not defective) × P (Part 2 not defective) × P (Part 1 not defective)

$=1-[(1-0.05)\times(1-0.10)\times (1-0.15)]\\=1-[0.95\times0.90\times0.85]\\=1-0.72675\\=0.27325\\\approx0.2733$

Thus, the probability that a product is defective is 0.2733.