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प्रश्न
A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be at least one defective item
उत्तर
Given n = 10
Probability of a defective item = p
= 5%
= `5/100`
∴ q = 1 – p
= `1 - 5/100`
= `95/100`
Let ‘X’ be the random variable denotes the number of defective items.
∴ Probability of ‘x’ successes in ‘n’ trials is
P(X = x) = nCx px qn-x
x = 0, 1, 2, ..., n
Probability that at least one defective item will e there
P(X ≥ 1) = 1 – P(X < 1)
= 1 – [P(X = 0)]
= `1 - [""^10"C"_0 (5/100)^0 (95/100)^(10 - 0)]`
= `1 - (95/100)^10`
= `1 - (0.95)^0`
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