Binomial Distribution vs Probability Distribution

A binomial setting has a fixed number of trials, two outcomes per trial, independent trials, and the same success probability each time. For example, the number of heads in 10 flips of a fair coin is binomial with $n = 10$ trials and success probability $p = 0.5$. The probability of exactly $k$ successes is $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ (n choose k, times p to the power k, times one minus p to the power n minus k). Its mean is $\mu = np$ (n times p).

A probability distribution shows how the total probability of $1$ is shared among a random variable's possible values. For example, rolling a fair six-sided die gives each value from 1 to 6 a probability of $\frac{1}{6}$. For a discrete variable the probabilities must satisfy $0 \le p_i \le 1$ and $\sum p_i = 1$ (each probability is between 0 and 1, and they add to 1). Continuous variables use a density curve instead, where probability is the area under the curve.