Define the following terms: a) Probability b) Independent events c) Dependent events

a) Probability

Probability is a measure of how likely an event is to occur. It is a real number between 0 (impossible) and 1 (certain).

For equally likely outcomes in a sample space $S$,

$$P(A) = \frac{|A|}{|S|}$$

where $|A|$ is the number of favorable outcomes for event $A$, and $|S|$ is the total number of possible outcomes.

b) Independent events

Two events $A$ and $B$ are independent if the occurrence of one does not affect the probability of the other.

Mathematically,

$$P(A \cap B) = P(A) \cdot P(B)$$

c) Dependent events

Two events $A$ and $B$ are dependent if the occurrence of one affects the probability of the other.

Mathematically,

$$P(A \cap B) \neq P(A) \cdot P(B)$$

or equivalently,

$$P(A \cap B) = P(A) \cdot P(B \mid A)$$