# Solve the following problem : A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of t - Mathematics and Statistics

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Solve the following problem :

A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of the retailer randomly selects 4 items from a shipment. Find the probability that the inspector finds at most one defective item in the 4 selected items.

#### Solution

Let X be the number of defective items.

P(an item is defective) = p = (10)/(100) = 0.1

∴ q = 1 – p = 1 – 0.1 = 0.9
Given, n = 4
∴ X ~ B(4, 0.1)
The p.m.f. of X is given by
P(X = x) = ""^4"C"_x (0.1)^x (0.9)^(4 - x), x = 0, 1, ...,4
P(at most one defective item)
= P(X ≤ 1)
= P(X = 0 or = 1)
= P(X = 0) + P(X = 1)
= ""^4"C"_0 (0.1)^0 (0.9)^4 + ""^4"C"_1 (0.1) (0.9)^3
= (0.9)4 + 4(0.1) (0.9)3
= 0.9477

Concept: Random Variables and Its Probability Distributions
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Part II | Q 1.06 | Page 156