The probability of a given event is 1/x . If the experiment is repeated n times, what is the probability that the event does not occur in any of the trials?

Question

8627 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-25T15:43:31

$((x-1)/x)^n$

Let say $p$ is the probability and event occurs and $q$ an event does not occur.

$p=1/x, q=1-(1/x)=(x-1)/x$

$P(X=r)="^nC_r*p^r*q^(n-r)$

r=0 when the event does not occur

$P(X=0)="^nC_0*(1/x)^0*((x-1)/x)^n$

$P(X=0)=1*1*((x-1)/x)^n$

$P(X=0)=((x-1)/x)^n$