How to compute Binomial Distribution? A basketball player scores a point in a free throw with 80% probability. Probability is independent of the result of the previous throw.
1) Given 5 free throws, find the probability distribution of the number of points scored by the player, and illustrate it by a histogram.
(I was thinking of fx(t) for t= 0, 1 with X~Bin(5, 0.8), but don't know how to compute to abtain the result! 
And simply have no idea how to generate the histogram! Do I computer the possibility for each of the 5 free throws? or possibility for the score 0 and 1? Have no idea how to get the individual possibility :'( )
2) What’s the probability that the player scores more than 200 points in free throws during the season?
(was thinking of P(X ≥ 200) but again don't know how to compute :'( )
3) During a season, the player performs 100 free throws. What’s the expected value of points scored in free throws during the season?
(am I right to compute as E(X) = np = 100*0.8 = 80? )
4) During a season, what’s the variance of the points scored in free throws?
(am I right to compute as Var(X) = np(1-p) = 100*0.8*(1-0.8) = 100*0.8*0.2 = 16? The result looks a bit awkward...)
Sorry for the dumb questions, I'm a novice to such problems and thus quite confused. Much appreciated for your explanation!
 A: If the random variable has a Binomial Distribution, that is it measures the successes in a series of Bernoulii trials, then the probability of obtaining some arrangement of $x$ successes and $n-x$ failures is given by:
$$X\sim \mathcal{Bin}(n, p) \;\iff\; \mathsf P(X=x) \,=\, \begin{cases}\dbinom{n}{x} p^x(1-p)^{n-x} &:x\in\{0\ldots n\}\\[1ex]0& : \text{else}\end{cases}$$
Use this to generate a histogram of $X\sim\mathcal{Bin}(5, 0.8)$ for $x$ in $\{0, 1, 2, 3, 4, 5\}$.
$$\text{Plot}\quad \mathsf P(X=x) \,=\, \dbinom{5}{x} 0.8^x\,0.2^{5-x} \quad\text{for}\quad x\in\{0\ldots 5\}$$

For large numbers of trials we typically use an approximation, such as the Normal approximation, or the Poisson approximation.   For this case I suggest normal approximation.
$$\mathcal{Bin}(n, p) \;\dot\sim\; \mathcal{N}(np, np(1-p))$$
Then use the Normal Tables (or an online calculator) to look up the relevant probabilities.
However you cannot compute, or even approximate, the probability of scoring more than 200 points unless you know the number of free throws in a season.
( If it is $100$ free throws, as in the follow up questions, the probability of scoring more than $200$ points is simply zero. )

For the remaining questions, where you are given a number of free throws to use, you have the right answers.  For a Binomial Distribution (or its approximation):
$$\begin{align}\mathsf E(X) &= np \\ \mathsf{Var}(X) &= np(1-p) \end{align}$$
