can someone clarify a doubt about this exercise: the literacy rate of a nation measures the proportion of people age 15 and over who can read and write A statistician is interested in the estimation of parameter $\theta$, the literacy rate for woman in Afghanistan and she has to choose between random samples from bernoulli or a geometric distribution (with the same $\theta$ ) i.e. given $n$ she can choose between the following exeperiments:
she randomly select $n$ afghani women and count the number of woman who are literate
she run $n$ different experiments, for each experiment, she keeps selecting woman until she finds a literate one; $Xi$ is the number of afghani woman she asks until one says she is literate
which of the 2 will give the more precise inference on $\theta$?
my attempt was to find the lowest variance between a bernoulli and geometric distribution to choose the more precise experiment through the inverse of fisher information Then I do not know how to choose the more precise
Any suggestion will be appreciate