GATE EC 2014 Set 4 — Question 37
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Engineering Mathematics → Probability → Bayes' Theorem
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Question
Parcels from sender S to receiver R pass sequentially through two post-offices. Each post-office has a probability of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post-office is_________.
Correct answer
0.43 to 0.45
Solution
Let be the event that the parcel is lost by the first post-office and be the event that the parcel is lost by the second post-office.
From the problem:
(where is the event that the parcel is not lost by the first office)The probability that the parcel is lost by the second post-office is:
The total probability that a parcel is lost () is the sum of the probabilities of it being lost at either office:
We are asked for the conditional probability that the parcel was lost by the second office, given that it was lost:
The value is approximately 0.44.
From the problem:
(where is the event that the parcel is not lost by the first office)The probability that the parcel is lost by the second post-office is:
The total probability that a parcel is lost () is the sum of the probabilities of it being lost at either office:
We are asked for the conditional probability that the parcel was lost by the second office, given that it was lost:
The value is approximately 0.44.
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