The items are packed in cartons of 10. Which one of the following statements is valid:Approximately 1 per cent of cartons will contain at least one defective itemThe probability of a carton containing 10 defective items is (0.01)¹⁰If the first item taken from a carton is defective there is a decreased probability that there will be another defective item in the cartonThe probability of a carton containing no defective items is 1 – (0.99)¹⁰
Question
The items are packed in cartons of 10. Which one of the following statements is valid:Approximately 1 per cent of cartons will contain at least one defective itemThe probability of a carton containing 10 defective items is (0.01)¹⁰If the first item taken from a carton is defective there is a decreased probability that there will be another defective item in the cartonThe probability of a carton containing no defective items is 1 – (0.99)¹⁰
Solution
The valid statement is: "The probability of a carton containing 10 defective items is (0.01)¹⁰".
Here's why:
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"Approximately 1 per cent of cartons will contain at least one defective item" - This statement is not necessarily valid because it assumes that the probability of a carton containing a defective item is 1%, which is not given in the problem.
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"The probability of a carton containing 10 defective items is (0.01)¹⁰" - This statement is valid. If the probability of one item being defective is 1% (or 0.01), then the probability of all 10 items in a carton being defective would be (0.01)¹⁰.
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"If the first item taken from a carton is defective there is a decreased probability that there will be another defective item in the carton" - This statement is not necessarily valid. The probability of finding a defective item does not change based on previous items unless it is stated that the defective items are not replaced.
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"The probability of a carton containing no defective items is 1 – (0.99)¹⁰" - This statement is not valid. The probability of a carton containing no defective items would be (0.99)¹⁰, not 1 – (0.99)¹⁰. The latter would be the probability of a carton containing at least one defective item.
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