Question

a company makes ballpoint pens ,the probability that a ball point point is defective is 0.02.what is the probability that sample of 400 ballpoint pens will contain exactly 5 defective ball point pens​

Answer 1

Given:

(i) The probability that a ballpoint pen is defective is 0.02.

To find:

(i) The probability that a sample of 400 ballpoint pens will contain exactly 5 defective ballpoint pens.

Solution:

Given, the probability a ballpoint pen is defective is (p) = 0.02.

So, the probability that a ballpoint pen is not defective (q) = 1-p  

= 1-0.02  

= 0.98

So, q = 0.98

We know, Proability P(x), is given as:

P(x)  = ⁿCₓpˣqⁿ⁻ˣ

where,

n = number of pens = 400

x = number of defective pens are present = 5

So, the probability 5 defective ballpoint pens will be present in a sample of 400 pens is:

P(5)  =   (⁴⁰⁰C₅)(0.02)⁵(0.98)³⁹⁵

= (⁴⁰⁰C₅)(1.09*10⁻¹²)

= 0.0907

≅ 0.091

So, the required probability is 0.091