We consider the problem of unbiased estimation of a finite population proportion and compare the relative efficiency of the unequal probability sampling strategies due to Horvitz and Thompson (1952) and Murthy (1957) under a super-population model. It is shown that the model expected variance is smaller for the Murthy's (1957) strategy both when these two sampling strategies are based on data obtained from (i) a direct survey, and (ii) a randomized response (RR) survey employing some RR technique following a general RR model.