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

A restaurant manager just installed a new dishwasher. He claims that

20%

of customers who have received a drink this week complained that the cup looked dirty.

If this pattern holds, and 4 more customers receive drinks this week, what is the probability that exactly 2 of the customers will complain that their cup looks dirty?

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

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question

A pharmaceutical company is developing a new test for gluten intolerance. The company is working to lower the "false positive rate" which is currently

23%

A false positive test result occurs when the test indicates someone is gluten intolerant, but in reality they are not.

If 2 volunteers were randomly selected to take the test, what is the probability that 0 will receive a false positive result?

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 choosing a volunteer to be tested.

Identify a success.

A trial is a success if the volunteer receives a false positive result. A trial is a failure if the volunteer does not receive a false positive result.

Find the probability.

The question describes a binomial experiment in which the number of trials is 2, the probability of success is 0.23, and the probability of failure is

–

0.23

0.77

Find the probability of exactly 0 successes using a binomial distribution with

0.23

and

0.77

(

)

–

0.23

0.77

–

0.5929

To the nearest thousandth,

(

)

≈

0.593

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Not feeling ready yet? These can help:

CC.2Combinations and permutations

DD.3Write a discrete probability distribution

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