Question

Components of a certain type are shipped to a supplier in batches of 10. 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. Given the condition that neither tested component is defective, what are the probabilities of the selected batch associated with 0, 1, and 2 defective components, respectively?

a) 0.5, 0.0, 0.0
b) 0.5, 0.3, 0.2
c) 0.3, 0.5, 0.2

Answer 1

The probability of selecting a batch with 0, 1, and 2 defective components can be calculated using conditional probability based on the given percentages.

Step-by-step explanation:

In this case, we are given that 50% of the batches contain no defective components, 30% contain one defective component, and 20% contain two defective components. We are also told that two components are randomly selected and tested, and neither of them is defective. We need to find the probability of the selected batch having 0, 1, and 2 defective components.

To calculate these probabilities, we need to use conditional probability. The probability of selecting a batch with 0 defective components is 50%, because 50% of the batches contain no defects. The probability of selecting a batch with 1 defective component is 30%, because 30% of the batches contain one defect. The probability of selecting a batch with 2 defective components is 20%, because 20% of the batches contain two defects.