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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

If the probability of success on each trial of an experiment is 0.4, what is the probability of 5 successes in 7 trials?

To determine

To calculate: The probability of 5 successes in 7 trials in an experiment.

Answer

Solution:

The probability of 5 successes in 7 trials in an experiment is 0.0774.

Explanation

Given Information:

The probability of success on each trial of an experiment is 0.4. Then The probability of 5 successes in 7 trials in an experiment.

Formula used:

For a binomial distribution the probability is,

Pr(x)=(Cxn)pxqnx

Where n the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.

q=1p

And,

Cxn=nxnx

Calculation:

Consider the probability of success on each trial of an experiment is p=0.4.

Then the probability of failure is,

q=1p=10.4=0.6

The probability of 5 successes in 7 trials in an experiment is,

Pr(x)=(Cxn)pxqnx

Where n=7,x=5,p=0.4,q=0.6

So,

Pr(x)=(C57)(0.4)5(0.6)75=(7575)(0.4)5(0.6)2=(752)(0.4)5(0.6)2=(76552)(0.01024)(0.36)

Thus,

Pr(x)=(762)(0.01024)(0.36)=(21)(0.01024)(0.36)=0.0774

Therefore, the probability of 5 successes in 7 trials in an experiment is 0.0774.

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