Question

Consider a binomial experiment with n = 9 trials where the probability of success on a single trial is p = 0.35. (Round your answers to three decimal places.) (a) Find P(r = 0).

Answer 1

Answer:

$P(X=0)$

And we can use the pmf and we got:

$P(X=0) = 9C0 (0.35)^0 (1-0.350)^{9-5}=0.1785$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=9, p=0.35)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

We want to find this probability:

$P(X=0)$

And we can use the pmf and we got:

$P(X=0) = 9C0 (0.35)^0 (1-0.350)^{9-5}=0.1785$