Question

Suppose a shipment of 130 electronic components contains 3 defective components. To determine whether the shipment should be​ accepted, a​ quality-control engineer randomly selects 3 of the components and tests them. If 1 or more of the components is​ defective, the shipment is rejected. What is the probability that the shipment is​ rejected?

Answer 1

In a 130 components 3 are defective and 127 non-defective.

Let x be the defective component,

P( X >= 1 ) = 1 - P( X = 0)

= 1 - P( none of 3 components are defective)

= 1 - ¹²⁷C₃ / ¹³⁰C₃

= 0.0682