This is a question that is not as straightforward as it may seem.
One could make arguments, some better than others perhaps, for several different answers. The way it is worded, one could defend answers from 0.000 and 1.000 and many of the intermediate numbers as well.
After four generations, what is the expected percentage of mitochondria from the original population of females that will still exist in the population’s children?
0.000; the original women died; THEIR mitochondria died as well. None of the original mitochondria still exist.
That may seem, and it largely is, a matter of semantics, but in some ways, it is true without word games. Every time the mitochondria split, the copies are not EXACTLY the same. The changes may be so minute they are not always detectable with the current technology, but that does not mean they do not exist.
Some changes occur to the underlying genome; they are rare and may not be readily observed, but that does not mean they do not exist as well. When one of these changes occur, all subsequent mitochondria will have the new genome assuming, of course, that the genome is viable.
If the change will not allow the cell to function properly, this will undoubtedly affect whether the child, as a whole organism, is able to survive. Depending on the severity of the malfunction that results from the new genome, it may make it more difficult, perhaps impossible, for the offspring to thrive, to mate, and to produce their own offspring which can accomplish the same.
It is also likely that some of these genetic mutations will result in change that is too minute to have an effect on the mitochondria or how it functions. By the same token, it is likely that eventually there will be a mutation in the mitochondrial genome that will have a marked effect on cell function. The change may even improve the overall function of the organism to an extent that will enable the offspring to thrive, to mate, and to produce their own offspring at a greater rate than organisms that do not have this change. Needless to say, the 'improved offspring' will pass on their 'improved genome' to the lucky offspring that will be more likely to thrive and pass it on to the next ..... etc.
There are many factors influencing how well the new genome is going to spread. The population in this particular question was somewhat isolated; this will encourage the genomic change to spread through the general population more quickly. The rate of the spread, however, is affected by many variables.
So in a world with no mutations or any other factors that can result in changed mitochondrial DNA, it would be 1.000 as every offspring gets its mothers, who got it from hers, who got it from hers, so the four types, on an isolated island, would remain four types.
However, in reality, changes do happen. An error(s) in transcription would be one of the most common, but certainly not the only, process that could result in any DNA being changed in a heritable manner.
There is an average rate of mutations. In fact, one can look at the mitochondrial DNA of two individuals and calculate how long ago the genomes were essentially the same. In other words, one could look at a mitochondrial genome from some ancient fossil and tell how many generations it likely took for it to evolve in to the genome of a particular modern individual. However, as these changes start as mistakes, it can take several generations for a change that is adaptive and will spread to occur.
The only way humans can observe these changes are in animals with very short life spans, such as fruit flies.
There would be very little change likely in only four generations; therefore, unless you had a very large sample size, any prediction would have little more than a theoretical chance to be correct.