Probability
The probability of something happening is a number from $0$ to $1$ that says how likely it is: $0$ means it cannot happen, and $1$ means it is certain.
Consider a random experiment, and collect every possible outcome of the experiment into a set, called the sample space. Think of the probability as a way of measuring the size of sets of outcomes, like area measures the size of regions, such that the whole sample space has size $1$. An event is a set of outcomes, and the probability of an event is the size of the event. For example, if you roll a fair die, then the sample space is $\setdef{1, 2, 3, 4, 5, 6}$, each outcome has size $\tfrac{1}{6}$, and the probability of the event “the roll is even,” which is $\setdef{2, 4, 6}$, is the size $\tfrac{1}{6} + \tfrac{1}{6} + \tfrac{1}{6} = \tfrac{1}{2}$.
Consider a probability space $(\Omega, \mathcal{F}, P)$. The probability of an event $A \in \mathcal{F}$ is the number $P(A)$ that the probability measure $P$ assigns to it.