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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 exactly two defective items?
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 exactly two defective item will be there
P(X = 2) = `""^10"C"_2 (5/100)^2 (95/100)^8`
= 10C2 (0.05)2 (0.95)8
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