# Probability of the union and the intersection of events

## Probability of the union of events

To compute the probability of the union of events, we have to check whether they are compatible or incompatible.

The probability of the union of incompatible events is: $$P(A\cup B)=P(A)+P(B)$$$The probability of the union of compatible events is: $$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$$

Note that when the events are incompatible $$P(A\cap B)=0$$, then the second formula is always true.

## Probability of the intersection of events

To calculate the probability of the intersection of events, we first have to verify whether they are dependent or independent.

The probability of the intersection of independent events is: $$P(A\cap B)=P(A)\cdot P(B)$$$The probability of the intersection of dependent events is: $$P(A\cap B)=P(A/B)\cdot P(B)$$$

Let's note that when the events are independent, $$P (A/B) = P (A)$$, then the second formula in fact is always true.