61. 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, 30% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What

(A2 ¨ B)

P(A ´ Bu C) 5 P(Au C) 1 P(Bu C) 2 P(A ¨ Bu C)

P(C) . 0 P(Br u A)

P(Bu A) . P(B) P(Br u A) , P(Br)

P(Au B) 1 P(Ar u B) 5 1 P(B) . 0 P(A1 ¨ A2 ¨ A3 u A1 ´ A2 ´ A3P(A2 ´ A3 ) u A1)

P(A2 ¨ A3 u A1P(A2 ) u A1)

A i 5 1, 2, 3 i 5 5awarded project i6 P(Bu A)

P(A) 5 .6 P(B) 5 .05 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. [Hint:
Draw a tree diagram with three first-generation branches for the three different types of batches.]