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Amoeba Colony (Posted on 2003-04-04) Difficulty: 4 of 5
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

See The Solution Submitted by Charlie    
Rating: 4.2000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Most of a Solution | Comment 3 of 4 |
(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
  Posted by Dulanjana on 2003-04-04 06:54:57

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