Question

If the probability of success during a single event of a geometric experiment is 0.34, what is the probability of success on the 6th event? Round your answer to the nearest tenth of a percent. A. 4.3% B. 6.5% C. 2.8% D. 9.8%

Answer 1

Answer: 4.3%

Explanation:

A P E X

Answer 2

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=
`q^(x-1)p`, where q = 1 - p

So, now

P =
`q^(x-1)p`

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 =
`q^(x-1)p`

=
`(0.66)^(6-1) * 0.34`

=
`(0.66)^(5) * 0.34`

= 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.