Finite Math Examples

Find the Probability P(x>0) of the Binomial Distribution x>0 , n=12 , p=0.30
, ,
Step 1
Subtract from .
Step 2
When the value of the number of successes is given as an interval, then the probability of is the sum of the probabilities of all possible values between and . In this case, .
Step 3
Find the probability of .
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Step 3.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 3.2
Find the value of .
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Step 3.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 3.2.2
Fill in the known values.
Step 3.2.3
Simplify.
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Step 3.2.3.1
Subtract from .
Step 3.2.3.2
Rewrite as .
Step 3.2.3.3
Cancel the common factor of .
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Step 3.2.3.3.1
Cancel the common factor.
Step 3.2.3.3.2
Rewrite the expression.
Step 3.2.3.4
Expand to .
Step 3.2.3.5
Divide by .
Step 3.3
Fill the known values into the equation.
Step 3.4
Simplify the result.
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Step 3.4.1
Evaluate the exponent.
Step 3.4.2
Multiply by .
Step 3.4.3
Subtract from .
Step 3.4.4
Subtract from .
Step 3.4.5
Raise to the power of .
Step 3.4.6
Multiply by .
Step 4
Find the probability of .
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Step 4.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 4.2
Find the value of .
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Step 4.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 4.2.2
Fill in the known values.
Step 4.2.3
Simplify.
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Step 4.2.3.1
Subtract from .
Step 4.2.3.2
Rewrite as .
Step 4.2.3.3
Reduce the expression by cancelling the common factors.
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Step 4.2.3.3.1
Cancel the common factor of .
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Step 4.2.3.3.1.1
Cancel the common factor.
Step 4.2.3.3.1.2
Rewrite the expression.
Step 4.2.3.3.2
Multiply by .
Step 4.2.3.4
Simplify the denominator.
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Step 4.2.3.4.1
Expand to .
Step 4.2.3.4.2
Multiply by .
Step 4.2.3.5
Divide by .
Step 4.3
Fill the known values into the equation.
Step 4.4
Simplify the result.
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Step 4.4.1
Raise to the power of .
Step 4.4.2
Multiply by .
Step 4.4.3
Subtract from .
Step 4.4.4
Subtract from .
Step 4.4.5
Raise to the power of .
Step 4.4.6
Multiply by .
Step 5
Find the probability of .
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Step 5.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 5.2
Find the value of .
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Step 5.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 5.2.2
Fill in the known values.
Step 5.2.3
Simplify.
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Step 5.2.3.1
Subtract from .
Step 5.2.3.2
Rewrite as .
Step 5.2.3.3
Cancel the common factor of .
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Step 5.2.3.3.1
Cancel the common factor.
Step 5.2.3.3.2
Rewrite the expression.
Step 5.2.3.4
Simplify the numerator.
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Step 5.2.3.4.1
Multiply by .
Step 5.2.3.4.2
Multiply by .
Step 5.2.3.5
Simplify the denominator.
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Step 5.2.3.5.1
Expand to .
Step 5.2.3.5.2
Multiply .
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Step 5.2.3.5.2.1
Multiply by .
Step 5.2.3.5.2.2
Multiply by .
Step 5.2.3.6
Divide by .
Step 5.3
Fill the known values into the equation.
Step 5.4
Simplify the result.
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Step 5.4.1
Raise to the power of .
Step 5.4.2
Multiply by .
Step 5.4.3
Subtract from .
Step 5.4.4
Subtract from .
Step 5.4.5
Raise to the power of .
Step 5.4.6
Multiply by .
Step 6
Find the probability of .
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Step 6.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 6.2
Find the value of .
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Step 6.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 6.2.2
Fill in the known values.
Step 6.2.3
Simplify.
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Step 6.2.3.1
Subtract from .
Step 6.2.3.2
Rewrite as .
Step 6.2.3.3
Cancel the common factor of .
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Step 6.2.3.3.1
Cancel the common factor.
Step 6.2.3.3.2
Rewrite the expression.
Step 6.2.3.4
Simplify the numerator.
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Step 6.2.3.4.1
Multiply by .
Step 6.2.3.4.2
Multiply by .
Step 6.2.3.4.3
Multiply by .
Step 6.2.3.5
Simplify the denominator.
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Step 6.2.3.5.1
Expand to .
Step 6.2.3.5.2
Multiply .
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Step 6.2.3.5.2.1
Multiply by .
Step 6.2.3.5.2.2
Multiply by .
Step 6.2.3.5.2.3
Multiply by .
Step 6.2.3.6
Divide by .
Step 6.3
Fill the known values into the equation.
Step 6.4
Simplify the result.
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Step 6.4.1
Raise to the power of .
Step 6.4.2
Multiply by .
Step 6.4.3
Subtract from .
Step 6.4.4
Subtract from .
Step 6.4.5
Raise to the power of .
Step 6.4.6
Multiply by .
Step 7
Find the probability of .
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Step 7.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 7.2
Find the value of .
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Step 7.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 7.2.2
Fill in the known values.
Step 7.2.3
Simplify.
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Step 7.2.3.1
Subtract from .
Step 7.2.3.2
Rewrite as .
Step 7.2.3.3
Cancel the common factor of .
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Step 7.2.3.3.1
Cancel the common factor.
Step 7.2.3.3.2
Rewrite the expression.
Step 7.2.3.4
Simplify the numerator.
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Step 7.2.3.4.1
Multiply by .
Step 7.2.3.4.2
Multiply by .
Step 7.2.3.4.3
Multiply by .
Step 7.2.3.4.4
Multiply by .
Step 7.2.3.5
Simplify the denominator.
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Step 7.2.3.5.1
Expand to .
Step 7.2.3.5.2
Multiply .
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Step 7.2.3.5.2.1
Multiply by .
Step 7.2.3.5.2.2
Multiply by .
Step 7.2.3.5.2.3
Multiply by .
Step 7.2.3.5.2.4
Multiply by .
Step 7.2.3.6
Divide by .
Step 7.3
Fill the known values into the equation.
Step 7.4
Simplify the result.
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Step 7.4.1
Raise to the power of .
Step 7.4.2
Multiply by .
Step 7.4.3
Subtract from .
Step 7.4.4
Subtract from .
Step 7.4.5
Raise to the power of .
Step 7.4.6
Multiply by .
Step 8
Find the probability of .
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Step 8.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 8.2
Find the value of .
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Step 8.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 8.2.2
Fill in the known values.
Step 8.2.3
Simplify.
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Step 8.2.3.1
Subtract from .
Step 8.2.3.2
Rewrite as .
Step 8.2.3.3
Cancel the common factor of .
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Step 8.2.3.3.1
Cancel the common factor.
Step 8.2.3.3.2
Rewrite the expression.
Step 8.2.3.4
Simplify the numerator.
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Step 8.2.3.4.1
Multiply by .
Step 8.2.3.4.2
Multiply by .
Step 8.2.3.4.3
Multiply by .
Step 8.2.3.4.4
Multiply by .
Step 8.2.3.4.5
Multiply by .
Step 8.2.3.5
Simplify the denominator.
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Step 8.2.3.5.1
Expand to .
Step 8.2.3.5.2
Multiply .
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Step 8.2.3.5.2.1
Multiply by .
Step 8.2.3.5.2.2
Multiply by .
Step 8.2.3.5.2.3
Multiply by .
Step 8.2.3.5.2.4
Multiply by .
Step 8.2.3.5.2.5
Multiply by .
Step 8.2.3.6
Divide by .
Step 8.3
Fill the known values into the equation.
Step 8.4
Simplify the result.
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Step 8.4.1
Raise to the power of .
Step 8.4.2
Multiply by .
Step 8.4.3
Subtract from .
Step 8.4.4
Subtract from .
Step 8.4.5
Raise to the power of .
Step 8.4.6
Multiply by .
Step 9
Find the probability of .
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Step 9.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 9.2
Find the value of .
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Step 9.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 9.2.2
Fill in the known values.
Step 9.2.3
Simplify.
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Step 9.2.3.1
Subtract from .
Step 9.2.3.2
Rewrite as .
Step 9.2.3.3
Cancel the common factor of .
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Step 9.2.3.3.1
Cancel the common factor.
Step 9.2.3.3.2
Rewrite the expression.
Step 9.2.3.4
Simplify the numerator.
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Step 9.2.3.4.1
Multiply by .
Step 9.2.3.4.2
Multiply by .
Step 9.2.3.4.3
Multiply by .
Step 9.2.3.4.4
Multiply by .
Step 9.2.3.5
Simplify the denominator.
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Step 9.2.3.5.1
Expand to .
Step 9.2.3.5.2
Multiply .
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Step 9.2.3.5.2.1
Multiply by .
Step 9.2.3.5.2.2
Multiply by .
Step 9.2.3.5.2.3
Multiply by .
Step 9.2.3.5.2.4
Multiply by .
Step 9.2.3.6
Divide by .
Step 9.3
Fill the known values into the equation.
Step 9.4
Simplify the result.
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Step 9.4.1
Raise to the power of .
Step 9.4.2
Multiply by .
Step 9.4.3
Subtract from .
Step 9.4.4
Subtract from .
Step 9.4.5
Raise to the power of .
Step 9.4.6
Multiply by .
Step 10
Find the probability of .
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Step 10.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 10.2
Find the value of .
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Step 10.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 10.2.2
Fill in the known values.
Step 10.2.3
Simplify.
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Step 10.2.3.1
Subtract from .
Step 10.2.3.2
Rewrite as .
Step 10.2.3.3
Cancel the common factor of .
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Step 10.2.3.3.1
Cancel the common factor.
Step 10.2.3.3.2
Rewrite the expression.
Step 10.2.3.4
Simplify the numerator.
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Step 10.2.3.4.1
Multiply by .
Step 10.2.3.4.2
Multiply by .
Step 10.2.3.4.3
Multiply by .
Step 10.2.3.5
Simplify the denominator.
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Step 10.2.3.5.1
Expand to .
Step 10.2.3.5.2
Multiply .
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Step 10.2.3.5.2.1
Multiply by .
Step 10.2.3.5.2.2
Multiply by .
Step 10.2.3.5.2.3
Multiply by .
Step 10.2.3.6
Divide by .
Step 10.3
Fill the known values into the equation.
Step 10.4
Simplify the result.
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Step 10.4.1
Raise to the power of .
Step 10.4.2
Multiply by .
Step 10.4.3
Subtract from .
Step 10.4.4
Subtract from .
Step 10.4.5
Raise to the power of .
Step 10.4.6
Multiply by .
Step 11
Find the probability of .
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Step 11.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 11.2
Find the value of .
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Step 11.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 11.2.2
Fill in the known values.
Step 11.2.3
Simplify.
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Step 11.2.3.1
Subtract from .
Step 11.2.3.2
Rewrite as .
Step 11.2.3.3
Cancel the common factor of .
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Step 11.2.3.3.1
Cancel the common factor.
Step 11.2.3.3.2
Rewrite the expression.
Step 11.2.3.4
Simplify the numerator.
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Step 11.2.3.4.1
Multiply by .
Step 11.2.3.4.2
Multiply by .
Step 11.2.3.5
Simplify the denominator.
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Step 11.2.3.5.1
Expand to .
Step 11.2.3.5.2
Multiply .
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Step 11.2.3.5.2.1
Multiply by .
Step 11.2.3.5.2.2
Multiply by .
Step 11.2.3.6
Divide by .
Step 11.3
Fill the known values into the equation.
Step 11.4
Simplify the result.
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Step 11.4.1
Raise to the power of .
Step 11.4.2
Multiply by .
Step 11.4.3
Subtract from .
Step 11.4.4
Subtract from .
Step 11.4.5
Raise to the power of .
Step 11.4.6
Multiply by .
Step 12
Find the probability of .
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Step 12.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 12.2
Find the value of .
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Step 12.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 12.2.2
Fill in the known values.
Step 12.2.3
Simplify.
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Step 12.2.3.1
Subtract from .
Step 12.2.3.2
Rewrite as .
Step 12.2.3.3
Reduce the expression by cancelling the common factors.
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Step 12.2.3.3.1
Cancel the common factor of .
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Step 12.2.3.3.1.1
Cancel the common factor.
Step 12.2.3.3.1.2
Rewrite the expression.
Step 12.2.3.3.2
Multiply by .
Step 12.2.3.4
Simplify the denominator.
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Step 12.2.3.4.1
Expand to .
Step 12.2.3.4.2
Multiply by .
Step 12.2.3.5
Divide by .
Step 12.3
Fill the known values into the equation.
Step 12.4
Simplify the result.
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Step 12.4.1
Raise to the power of .
Step 12.4.2
Multiply by .
Step 12.4.3
Subtract from .
Step 12.4.4
Subtract from .
Step 12.4.5
Raise to the power of .
Step 12.4.6
Multiply by .
Step 13
Find the probability of .
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Step 13.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 13.2
Find the value of .
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Step 13.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 13.2.2
Fill in the known values.
Step 13.2.3
Simplify.
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Step 13.2.3.1
Subtract from .
Step 13.2.3.2
Rewrite as .
Step 13.2.3.3
Cancel the common factor of .
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Step 13.2.3.3.1
Cancel the common factor.
Step 13.2.3.3.2
Rewrite the expression.
Step 13.2.3.4
Expand to .
Step 13.2.3.5
Divide by .
Step 13.3
Fill the known values into the equation.
Step 13.4
Simplify the result.
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Step 13.4.1
Raise to the power of .
Step 13.4.2
Multiply by .
Step 13.4.3
Subtract from .
Step 13.4.4
Subtract from .
Step 13.4.5
Evaluate the exponent.
Step 13.4.6
Multiply by .
Step 14
Find the probability of .
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Step 14.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 14.2
Find the value of .
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Step 14.2.1
Find the number of possible unordered combinations when items are selected from available items.
Step 14.2.2
Fill in the known values.
Step 14.2.3
Simplify.
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Step 14.2.3.1
Cancel the common factor of .
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Step 14.2.3.1.1
Cancel the common factor.
Step 14.2.3.1.2
Rewrite the expression.
Step 14.2.3.2
Simplify the denominator.
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Step 14.2.3.2.1
Subtract from .
Step 14.2.3.2.2
Expand to .
Step 14.2.3.3
Divide by .
Step 14.3
Fill the known values into the equation.
Step 14.4
Simplify the result.
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Step 14.4.1
Multiply by .
Step 14.4.2
Raise to the power of .
Step 14.4.3
Subtract from .
Step 14.4.4
Subtract from .
Step 14.4.5
Anything raised to is .
Step 14.4.6
Multiply by .
Step 15
The probability is the sum of the probabilities of all possible values between and . .
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Step 15.1
Add and .
Step 15.2
Add and .
Step 15.3
Add and .
Step 15.4
Add and .
Step 15.5
Add and .
Step 15.6
Add and .
Step 15.7
Add and .
Step 15.8
Add and .
Step 15.9
Add and .
Step 15.10
Add and .
Step 15.11
Add and .