Statistical Inference — consistent estimators from Bernoulli trials

Consider a series of Bernoulli trials with probability of success $p$ $(0 < p < 1)$ for each trial, such that $f$ is frequency of success in $n$ trials. Consider the following statements: I. $\frac{f}{n}\left(1-\frac{f}{n}\right)$ is a consistent estimator of $p(1-p)$. II. $\frac{f}{n}$ is a consistent estimator of $\frac{1}{p}$. Which of the statements given above is/are correct?