Question

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 31% contain one defective component, and 20% 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? (Round your answers to four decimal places.)

(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.]

Answer 1

Let B0 shows the event that batch with zero defective is selected. B1 shows the event that batch with one defective is selected. B2 shows the event that batch with two defectives is selected.

From the given information we have,

(a)

Let D shows the event that no defective is found out of 2 items.

If batch contains no defective so

If batch contains one defective (that is 9 non defective) and our selected components have no defective then

If batch contains two defectives (that is 8 non defective) and our selected components have no defective then

Using law of total probability, the probability that selected components have no defective is

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(b)

Let D shows the event that one defective is found out of 2.

If batch contains no defective so

When batch contains one defective (that is 9 non defective) and our selected components have one defective then

When batch contains two defectives (that is 8 non defective) and our selected components have one defective then

Using law of total probability, the probability that selected components have no defective is

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