A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials

Aydan Hardy

Aydan Hardy

Answered question

2023-03-31

A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.n=20​,
p=0.7​,
x=19
P(19)=

Answer & Explanation

gatumisz3f6

gatumisz3f6

Beginner2023-04-01Added 4 answers

To calculate the probability of having 19 successes in 20 independent trials of a binomial probability experiment, we can use the binomial probability formula:
P(x)=(nx)·px·(1p)nx,
where n represents the number of trials, x is the number of successes, and p is the probability of success in a single trial.
Given:
n=20 (number of independent trials)
p=0.7 (probability of success in a single trial)
x=19 (number of successes)
Now, let's substitute these values into the formula and calculate the probability:
P(19)=(2019)·0.719·(10.7)2019.
The binomial coefficient, (2019), can be calculated as:
(2019)=20!19!(2019)!.
Simplifying this expression, we have:
(2019)=20!19!·1!=20.
Now, let's substitute the calculated values into the probability formula:
P(19)=20·0.719·(10.7)2019.
Calculating the exponents:
P(19)=20·0.719·0.31.
Simplifying the expression:
P(19)=20·0.719·0.3.
Now, let's calculate the numerical value of this probability:
P(19)=20·0.719·0.30.00684.
Therefore, the probability of having 19 successes in 20 independent trials of the binomial probability experiment is approximately 0.00684.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school probability

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?