Since, the probability of success during a single event of a geometric experiment is 0.34.
We have to find the probability of success on the 6th event.
Since it is a geometric experiment. So, when a discrete random variable 'X' is said to have a geometric distribution then it has a probability density function (p.d.f.) of the form:
P= [tex] q^{x-1}p [/tex], where q = 1 - p
So, now
P = [tex] q^{x-1}p [/tex]
where 'p' is the probability of success and 'q' is the probability of failure and x is the number of events.
Since the probability of success (p)is 0.34
Therefore, probability of failure(q)= 1 - p
= 1 - 0.34
= 0.66
and x = 6
So, P = [tex] q^{x-1}p [/tex]
= [tex] (0.66)^{6-1} \times 0.34 [/tex]
= [tex] (0.66)^{5} \times 0.34 [/tex]
= 0.0425
So, the nearest tenth of a percent of probability of success on the 6th event =
4.257 %
Rounding to the nearest tenth, we get
= 4.3%
So, Option A is the correct answer.
