John makes random guesses on his multiple-choice test, which has five options for each question. let the random variable x be the number of guesses taken before guessing correctly.

assuming the guesses are independent, find the probability that he doesn't guess correctly until his 6th guess.

0.0655

0.0789

0.3521

0.3277

So the correct option would be:

0.0655

Step-by-step explanation:

Previous concepts

A negative binomial random variable "is the number X of repeated trials to produce r successes in a negative binomial experiment. The probability distribution of a negative binomial random variable is called a negative binomial distribution, this distribution is known as the Pascal distribution".

And the probability mass function is given by:

Where r represent the number successes after the x trials and p is the probability of a success on any given trial.

Solution to the problem  

Let X the random variable that represent the number of guesses taken before guessing correctly.

For this case the random variable X follows a negative binomial distribution given by:

And we want to find the probability P(X=1) and if we replace in the mass function we got:

So the correct option would be:

0.0655

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

my dear correct answer is option number 3