Quick questions on Statistical distributions: discrete random variables and the binomial distribution - Edexcel A-Level Maths

A discrete random variable $X$ has a probability distribution that lists each value with its probability, and the probabilities must add to $1$. For example, a distribution might assign $P(X = 1) = 0.2$, $P(X = 2) = 0.5$ and $P(X = 3) = 0.3$.

A handy memory aid is the four letters in "BINS": a Binomial needs Independent trials, a fixed Number of trials, and a constant Success probability. Sampling with replacement keeps $p$ constant and the trials independent, so it is binomial; sampling without replacement changes $p$ from trial to trial, so it is not. The single value $P(X = r)$ uses the formula directly, whereas a phrase like "at most", "fewer than" or "at least" calls for a cumulative probability, often read straight from a calculator's cumulative binomial function.

State the two distribution parameters and the mean of $X \sim B(20, 0.1)$. [2 marks]

For $X \sim B(8, 0.5)$, find $P(X = 4)$. [3 marks]