And Rule (multiplication) / Or Rule (addition for mutually exclusive events)

Understanding the And Rule

The And Rule in probability concerns itself with two events happening at the same time - for example, flipping a coin and getting heads and also rolling a die and landing on a 6.
The rule is formed on multiplication. If you want to know the probability of two events happening at the same time, multiply their individual probabilities together.
This only works when the events are independent - that means the outcome of one event does not affect the outcome of the other.
For example, if event A has a probability of 0.5 and event B has a probability of 0.2, then the probability of both events (A and B) taking place is 0.5 x 0.2 = 0.1 or 10%.

The Or Rule in probability deals with one event or another happening - for example, flipping a coin and getting heads or also rolling a die and landing on a 6.
The rule is based on addition. If you want to know the probability of one event or another event happening, add their individual probabilities together.
However, this rule only strictly applies when the events are mutually exclusive - this means they cannot happen at the same time.
For example, if event A has a probability of 0.5 and event B has a probability of 0.2, then the mutually exclusive probability of event A or B happening is 0.5 + 0.2 = 0.7 or 70%.

In some cases, you might have to use both the And Rule and the Or Rule to solve complex probability problems.
For example, if you’re looking at the likelihood of getting heads on a coin flip and rolling a six on a die (multiplication/And Rule) or drawing an ace from a deck of cards (addition/Or Rule).
Always make sure you understand whether the events in question are independent or mutually exclusive before deciding which rule to use.

The total probability of all possible outcomes should always sum to one (or 100%). If it’s less than or more than this, make sure to check your calculations.
Visualising these examples with Venn diagrams or tree diagrams can also be a helpful way to better understand them.