GATE ME 2016 Set 2 — Question 38
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Question
The probability that a screw manufactured by a company is defective is 0.1. The company sells screws in packets containing 5 screws and gives a guarantee of replacement if one or more screws in the packet are found to be defective. The probability that a packet would have to be replaced is _________
Correct answer
0.39 to 0.43
Solution
Let be the probability that a screw is defective, .
The probability that a screw is not defective is .
The number of screws in a packet is .
A packet is replaced if one or more screws are defective ().
Using the binomial distribution, the probability that a packet is replaced is:
Thus, the probability that a packet would have to be replaced is approximately 0.41, which falls within the range [0.39, 0.43].
The probability that a screw is not defective is .
The number of screws in a packet is .
A packet is replaced if one or more screws are defective ().
Using the binomial distribution, the probability that a packet is replaced is:
Thus, the probability that a packet would have to be replaced is approximately 0.41, which falls within the range [0.39, 0.43].
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