A large chain retailer purchases a certain kind of electronic device from a manufacture. The manufacturer indicates that the defective rate of the device is 15%. The inspector randomly picks 10 items from a shipment. What is the probability that there will be at least one defective item among these 10?

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Solution:

Let, x = no. of defective items

By questions, n = 10

Probability of defective (p) = 15% = 0.15

∴ q = 1 – p

= 1 – 0.15

= 0.85

p(x) = nCx . px . qn-x

Now, probability of least one defective among these 10 is

p(x ≥ 1) = 1 – p(x < 1)

= 1 – p(x = 0)

= nCx . px . qn-x

= 1 – 10C0 . (0.15)0 .  (0.85)10

= 0.80

∴ 80% is the probability that there will be at least one defective item among these 10.

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