  It is known that the time until a birth and death process reaches a certain
level is distributed as a sum of independent exponential random variables.
Diaconis, Miclo and Swart gave a probabilistic proof of this fact by coupling
the birth and death process with a pure birth process such that the two
processes reach the given level at the same time. Their coupling is of a
special type called intertwining of Markov processes. We apply this technique
to couple the Wright-Fisher diffusion with reflection at 1/2 and a pure birth
process. We show that in our coupling the time of absorption of the diffusion
is a.s. equal to the time of explosion of the pure birth process. The coupling
also allows us to interpret the diffusion as being initially reluctant to get
absorbed, but later getting more and more compelled to get absorbed.
