IXL - Find probabilities using the binomial distribution (Geometry practice)

Caden researches animal behavior. He teaches monkeys to push a button in order to receive a treat.

25%

of the time, a monkey receives kiwi as the treat.

If a monkey presses the button 4 times, what is the probability that it will receive kiwi as a treat exactly 4 times?

Write your answer as a decimal rounded to the nearest thousandth.

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question

Tracy hosts a trivia night at her house every Thursday. She generates questions using a trivia website. The website claims that there is a

62%

chance that a generated question is a history question.

If the claim is correct, and Tracy randomly generates 4 questions during the first round of trivia, what is the probability that exactly 3 will be history questions?

Write your answer as a decimal rounded to the nearest thousandth.

key idea

A binomial experiment consists of identical and independent trials. In each trial there are two outcomes: success and failure.

In a binomial experiment, the number of successes is a random variable. Its probability distribution is called the binomial

distribution.

The binomial distribution depends on

the number of trials, and

the probability of success. The probability of exactly

successes is:

(

)

(

–

)

–

Sometimes 1 -

the probability of failure, is written as

(

)

–

solution

Interpret the situation as a binomial experiment.

Identify the trials.

A trial is generating a trivia question.

Identify a success.

A trial is a success if the question is a history question. It is a failure if the question is not a history question.

Find the probability.

The question describes a binomial experiment in which the number of trials is 4, the probability of success is 0.62, and the probability of failure is

–

0.62

0.38

Find the probability of exactly 3 successes using a binomial distribution with

0.62

and

0.38

(

)

–

0.62

0.38

–

0.238328

0.38

0.36225856

To the nearest thousandth,

(

)

≈

0.362

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