Is it 4/9?

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Parcels from sender to receiver pass sequentially through 2 post office.Each post office has a probability 1/5 of loosing an incoming parcel,independently of all other parcels.Given that a parcel is lost, the probabilty that it was lost by the second post office is....??

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Probability

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There are two post offices and probability of losing parcel by P1=1/5 and P2=1/5

It is a case of conditional probability

Case 1:parcel lost in P1(1st post office) =1/5 If parcel is lost by P1, it will not reach P2 hence no probability of P2 has to be considered

Case 2: parcel lost in P2: this ensures that parcel has not been lost at P1=(1-1/5)*1/5

(1-1/5)=4/5 probability that parcel is not lost by P1

According to the given question, probability that parcel is lost by P2=

(4/5*1/5)/((1/5)+(4/5*1/5)=4/9

It is a case of conditional probability

Case 1:parcel lost in P1(1st post office) =1/5 If parcel is lost by P1, it will not reach P2 hence no probability of P2 has to be considered

Case 2: parcel lost in P2: this ensures that parcel has not been lost at P1=(1-1/5)*1/5

(1-1/5)=4/5 probability that parcel is not lost by P1

According to the given question, probability that parcel is lost by P2=

(4/5*1/5)/((1/5)+(4/5*1/5)=4/9

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