A random experiment consists of throwing 100 fair dice, each die having six faces numbered 1 to 6 . An event $A$ represents the set of all outcomes where at least one of the dice shows a 1 . Then, $\mathrm{P}(\mathrm{A})=$

Consider a coin-toss experiment where the probability of head showing up is $p$. In the $i^{\text {th }}$ coin toss, let $X_i=1$ if head appears, and $X_i=0$ if tail appears.

Consider

$$ \hat{p}=\frac{1}{n} \sum_{i=1}^n X_i $$

where $n$ is the total number of independent coin tosses.

Which of the following statements is/are correct?

A bag contains 5 white balls and 10 black balls. In a random experiment, $n$ balls are drawn from the bag one at a time with replacement. Let $S_n$ denote the total number of black balls drawn in the experiment.

The expectation of $S_{100}$ denoted by $E\left[S_{100}\right]=$ ___________ (Round off to one decimal place)