Finite Math Examples

Find the Probability P(x<1) of the Binomial Distribution
, ,
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
Simplify the numerator.
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Step 3.2.3.1.1
Expand to .
Step 3.2.3.1.2
Multiply by .
Step 3.2.3.2
Simplify the denominator.
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Step 3.2.3.2.1
Expand to .
Step 3.2.3.2.2
Subtract from .
Step 3.2.3.2.3
Expand to .
Step 3.2.3.2.4
Multiply by .
Step 3.2.3.2.5
Multiply by .
Step 3.2.3.3
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
Multiply by .
Step 3.4.2
Anything raised to is .
Step 3.4.3
Multiply by .
Step 3.4.4
Subtract from .
Step 3.4.5
Subtract from .
Step 3.4.6
Raise to the power of .
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