Each week, a prisoner is given five black chips and five white chips to distribu

Question

Each week, a prisoner is given five black chips and five white chips to distribute however he wishes between two urns, as long as each urn gets at least one chip. The jailer will then pick one urn at random and draw one chip from that urn. If the chip is white, the prisoner goes free. If the chip is black, the prisoner is fed to very hungry dogs.

If every prisoner puts one white chip in one urn and rest of the chips into the other, what is the probability that the very hungry dogs will have to wait at least eight weeks to enjoy one delicious prisoner-meal?

Explanation / Answer

put one white chip in Urn 1, and the other 9 in Urn 2.

Then his probability of survival would be 1/2 + 1/2*(4/9)=0.722

They have to survive atleast for 8 weeks

so probablity of survival for 8 weeks=(0.733)^8=0.0833

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