If we have two independent events, $A$ and $B$, what is the probability they both occur? In other words, what is...

$$A \ and \ B$$

The Venn Diagram Reveals All

If we're throwing a dart, what is the probability we land in the overlapping space? How do we calculate the size of that "middle portion"?

The Formula

It's actually pretty straightforward. You simply multiply the probabilities of $A$ and $B$ together. But remember, this ONLY works in independent events.

$$A \ and \ B = A \times B$$

Example

What is the probability of rolling a prime number on a fair, $6$-sided die and flipping heads on a fair coin?

Probability of rolling a prime number: $\frac{3}{6} = 0.50$

Probability of flipping heads: $\frac{1}{2} = 0.50$

Probability of both happening:

$$0.50 \times 0.50 = 0.25$$