The probability that a part produced by a certain factorys a

The probability that a part produced by a certain factory\'s assembly line will be defective is 0.013. Find the probabilities that in a run of 47 items, the following results are obtained. a. Exactly 3 defective items b. No more than 2 defective items c. At least 1 defective item

Solution

solution:

p(D)=0.013

p(nD)=1-0.013=0.987

a) for 3 defective items= C⁴⁷₃(0.013)³(0.987)⁴⁴

b) for not more than 2 defective iterms

possible cases

no items defective or 1 item defective or 2 items defective

hence probablity=C⁴⁷₀(0.013)⁰(0.987)⁴⁷ +C⁴⁷₁(0.013)¹(0.987)⁴⁶+C⁴⁷₂(0.013)²(0.987)⁴⁵

^c) probablity of atleast 1 item defective= 1-(prob of no items defective)

=1-C⁴⁷₀(0.013)⁰(0.987)⁴⁷