Probability

Question

Parcels from sender S to receiver R pass sequentially through two post offices. Each post office has a probability 1/5 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 ?

Comments

is it 4/9 ?

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Yes, correct.

Explain your answer.

Answer 1

Expected probablity

= P(parcel lost by 2nd post office/ parcel is lost)

=  P(parcel is lost by 2nd post office $\cap$ parcel is lost) / P(parcel is lost)  

= { P(parcel is lost / parcel arrives at second post office) * P(parcel arrives at second post office) }

   / { P(parcel is lost/parcel arrives at 1st post office) * P(parcel arrives at 1st post office)

      * P(parcel is lost/parcel arrives at 2nd post office) * P(parcel arrives at 2nd post office) }

= { 1/5 * 4/5 } / {1/5 * 1  +   1/5 * 4/5  }

= 4/9

Comments

okay..thanks

Answer 2

 Question is about total probability.