Suppose we run an experiment and the result can be either positive (with fixed probability p) and negative (with fixed probability 1 - p). We wish to estimate the unknown p by doing the following: we run the above experiment repeatedly and independently until we get 2 positives, then we stop. That is, we stop running the experiments when we reach the 2nd positive. Suppose we have to run this experiment 7 times to get to the 2nd positive.

(a) Express the probability of observing the above results (i.e., experiment 7 times to get 2nd positive) as a function of p.

(b) Based on part (a), find an estimate of the unknown value of p.