Thread: Absorbing Markov Chain

You have five fair coins. You toss them all so that they randomly fall heads or tails. Those that fall tails in the first toss you pick up and toss again. You toss again those that show tails after the second toss, and so on, until all show heads. Let X be the number of coins involved in the last toss. Find Pr{X=1}

Hey thanhloc192.

This looks like a typical Gamblers Ruin type problem, but an even simpler approach would be to ask if the process always terminates.

If you have a non-zero chance of getting a heads, then what does this say about whether the process terminates and if so how does relate to P(X=1) when X is the number of flips when the process terminates?