Answer to Question #101769 in Statistics and Probability for Rajesh shrimali

Question

A manufacturer knows that the razor blades he makes contain on an average 0.5% of defectives. he packs them in packs of 5 what's the probability that a packet picked at random will contain 3 or more faulty blades ?

Answer 1

Probability of defect p = 0.5% = 0.005

q = 1 - p = 1 - 0.005 = 0.995

Now the number of packs is n = 5.

We need to find probability of 3 or more faulty blades.

$P(x \geq 3)=P(x=3)+P(x=4)+P(x=5)$ P(x >= 3)

= ⁵C₃ 0.005³ * 0.995² + ⁵C₄ 0.005⁴*0.995 + ⁵C₅ * 0.005⁵

= 0.000001238 + 0.000000003 + 3.125 * 10^-12

= 1.241 * 10^-6