Question

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 50% of all such batches contain no defective components, 35% contain one defective component, and 15% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions?
a. Neither tested component is defective.
b. One of the two tested components is defective

Answer 1

Answer:

a) P (0 defective component) = 0.5

   P( 1 defective component ) = 0.35

    P( 2 defective component ) = 0.15

b) P( 0 ) = 0

   p ( 1 ) =  1

   p ( 2 ) = 0.33

Step-by-step explanation:

p( no defective ) = 0.5

p( 1 is defective ) = 0.35

p( 2 is defective ) = 0.15

Given that 2 components are selected at random

a) Given that neither component is defective

Probability of 0 defective component = 0.5

P( 1 defective component ) = 0.35

P( 2 defective component ) = 0.15

b) Given that one of the two tested component is defective

P( 0 defective ) = 0

P( 1 defective ) = P ( $\frac{x=1}{x\geq 1}$ ) = p( x = 1 ) / 1 - P ( x = 0 )

                                        = ( 0.5 )^1 ( 0.5 )^0 /  1 - ( 0.5)^0 (0.5)^1

                                        = 0.5 * 1 / 1 - 0.5 = 0.5 / 0.5 =  1

p ( 2 defective ) = p( x = 3 ) / 1 - P ( x = 0 )

                         = ( 0.5 )^2 ( 0.5 )^0 /  1 - ( 0.5)^0 (0.5)^2

                         = 0.25 / 0.75 = 0.33