# Given the probability p=87/100 that an event will not happen, how do you find the probability that the event will happen?

Mar 7, 2017

See the entire solution process below:

#### Explanation:

If this is truly a binary event (either the event will happen or the event will not happen, there are not other options) then the probability of the event happening and the probability of the event not happening is 100% or $\frac{100}{100}$

Therefore, the probability of the event happening, let's call it ${p}_{h}$ is equal to $\frac{100}{100}$ minus the probability of the event not happening, let's call it ${p}_{n}$

Or:

${p}_{h} = \frac{100}{100} - {p}_{n}$

We know ${p}_{n} = \frac{87}{100}$ so we can substitute and solve for ${p}_{h}$L

${p}_{h} = \frac{100}{100} - \frac{87}{100} = \frac{100 - 87}{100} = \frac{13}{100}$

The probability of the event happening is $\frac{13}{100}$