Question

A manufactured item 4 defective with probability p = .001. What is the probability that a lot of 1000 items will have no more than 1 defective itern.

Answer 1

Answer:

0.999^999 × 1.999

≈ 0.7357589 (approx)

Step-by-step explanation:

P(0 defective items)

= P(item 1 okay) × P(item 2 okay) × ... × P(item 1000 okay)

= ( 1 - 0.001 )^1000

= 0.999^1000

P(1 defective item)

= (# ways of selecting which one is defective) × P(that one is defective) × P(each of the remaining 999 are okay)

= 1000 × 0.001 × ( 1- 0.001 )^999

= 0.999^999

P(no more than 1 defective item)

= P(0 defective items) + P(1 defective item)

= 0.999^1000 + 0.999^999

= 0.999^999 × ( 0.999 + 1 )

= 0.999^999 × 1.999

≈ 0.7357589 (approx)