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?

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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#