GATE 2016 ME (ME2) – Question 38
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 ______.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.39 to 0.43
Explanation
Assuming independent defects, the probability that all five screws are satisfactory is0.9⁵=0.59049. A replacement is needed for the complementary event of at least one defect. Therefore probability is1−0.59049=**0.40951**. Adding five individual defect probabilities would double-count packets with multiple defects.