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?

1 Answer
Jan 25, 2017

((x-1)/x)^n

Explanation:

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