a. If the batch from which the components were selected actually contains two defective components, what is the probability that neither of these is selected for testing? b. What is the probability that the batch contains two de- fective components and that neither of these is selected for testing? c. What is the probability that neither component selected for testing is defective? (Hint: This could happen with any one of the three types of batches. A tree diagram might help.)

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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Components of a certain type are shipped to a supplier in batches of 10. Suppose that 50% of all batches contain no defective components, 30% contain one defec- tive component, and 20% contain two defective compo- nents. A batch is selected at random. Two components from this batch are randomly selected and tested.

a. If the batch from which the components were selected actually contains two defective components, what is the probability that neither of these is selected for testing?
b. What is the probability that the batch contains two de- fective components and that neither of these is selected for testing?

c. What is the probability that neither component selected for testing is defective? (Hint: This could happen with any one of the three types of batches. A tree diagram might help.)

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