Solution
= Solution
Write $N=\sum_{j=1}^{10}X_j$, where the independent <Bernoulli random variables> indicate rottenness. Since $X_j^2=X_j$, their <variances> are $E[X_j^2]-E[X_j]^2=p-p^2$. The <independence> makes all cross <covariances> zero, so
$$
\operatorname{Var}(N)=10p(1-p),\qquad\boxed{\sigma_N=\sqrt{10p(1-p)}\text{ pieces}.}
$$
This <standard deviation> vanishes at $p=0$ and $p=1$, when the count is certain.