Question

It is known that screws produced by a certain company will be defective with probability .01, independently of each other. The company sells the screws in packages of 10 and offers a moneyback guarantee that at most 1 of the 10 screws is defective. What proportion of packages sold must the company replace?

Answer 1

Given in the question that replacement guarantee is offered if at most 1 of 10 screws is defective.So the probability of this to occur is :

   P(x = 0) + P(x = 1)

 =  10C0 * (0.99)10 +  10C1(0.01)(0.99)9  

 = 0.9957

 = 99.57 %

(Had the probability been asked for replacement guarantee if at least 2 are defective it would have been 0.43 % but here we are given at most one which is coming out to be 99.57%

Answer 2

Explanation:

take this known that screws produced by a certain company will be defective with probability .01, independently of each other. The company sells the screws in packages of 10 and offers a moneyback guarantee that at most 1 of the 10 screws is defective. What proportion of packages sold must the company replace?