This problem deals with an elementary aspect of a simple branching process. A population starts with one member; at time t = 1, it either divides with probability p or dies with probability 1 − p. If it divides, then both of its children behave independently with the same two alternatives at time t = 2. What is the probability that there are no members in the third generation? For what value of p is this probability equal to .5?
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