# Given the probability p=13/20 that an event will not happen, how do you find the probability that the event will happen?

Apr 24, 2017

$1 - \frac{13}{20} = \frac{7}{20}$

#### Explanation:

For any given event, there are only two outcomes:
Either the event DID happen or it DID NOT happen.
(It cannot almost happen, or half happen)

The sum of the probabilities in a given situation is always $1$

$P \left(\text{event happens") +P("even does not happen}\right) = 1$

$P \left(\text{even does happen") = 1 - P("even does not happen}\right)$

$P \left(\text{even does happen}\right) = 1 - \frac{13}{20} = \frac{7}{20}$