For numerical answers, the following forms are acceptable: fractions, decimals, symbolic e.g.:$\left( \begin{array}{c} n \\ r \end{array} \right)^n P_r , n!$ etc.
$\text{Description for the following question:}$
Suppose $X$ is the number of successes out of $n$ trials, where the trials are independent of each other. The probability of success of every trial is $p$. The probability that there will be exactly $k$ successes out of n trials is
$$\mathbb{P}(X=k)=\left( \begin{array}{c} n \\ k \end{array} \right) p^k (1-p)^{n-k}, k=0,1,…,n.$$
The expected number of success is $\mathbb{E}(X)=np$.
For the situation in the previous problem, what is the expected number defaults?
