GATE 2024 MN – Question 45
Mines M 1, M 2, M 3 supply 60%, 25%, 15% of coal. Their probabilities of below-Grade 1 wagons are 0.02, 0.03, 0.04. A sampled wagon is below Grade 1. Find probability it came from M 1, to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.42 to 0.52
Explanation
Bayes’ rule gives P(M 1|bad)=0.60×0.02 divided by the total bad-wagon probability. That denominator is 0.012+0.0075+0.006=0.0255. Ratio 0.012/0.0255=0.470588, or 0.47. The observed defect changes the supplier proportions.