GATE 2022 PI – Question 58
A factory uses 100 bulbs and individually replaces failures at ₹300 each. Cumulative failure probabilities at 1,2,3,4,5 months are 0.10,0.25,0.47,0.68,1.00. Find expected monthly replacement cost in rupees, nearest integer.
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Correct answer: 8570 to 8701
Explanation
Lifetime probabilities are successive differences: 0.10,0.15,0.22,0.21,0.32. Expected life = 1×0.10+2×0.15+3×0.22+4×0.21+5×0.32 = 3.50 months. Long-run monthly cost = 100×300/3.50 = 8571.43, rounding to **₹8571**.