GATE 2014 EC (EC4) – Question 37
A parcel goes sequentially through two post offices from S to R. Each independently loses an incoming parcel with probability 1/5. Given that a parcel is lost, find the probability it was lost at the second office.
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Correct answer: 0.43 to 0.45
Explanation
A parcel is lost at the second office only if it survives the first:probability(4/5)(1/5)=4/25. Total loss probability is1−(4/5)²=9/25. Conditional on a loss, the second-office probability is(4/25)/(9/25)=**4/9≈0.444444**. Losses at the two offices are mutually exclusive for the same parcel.