A colony of amoebae is started by placing one amoeba in a petri dish. In any given minute, each amoeba present at the time may do one of four things with equal probability (i.e., 1/4):

1. Die, leaving no progeny.

2. Continue to live, but not split.

3. Split into 2.

4. Split into 3.

What is the probability that the colony will die out, rather than take hold and continue forever?

adapted from braingle at http://www.braingle.com/teaser.php?id=8705&op=&comm=1

(In reply to

re: Most of a Solution by friedlinguini)

it should be p² + 2p - 1 = 0

Therefore (p - 1)² = 0

Hence p = 1