# 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 .
Step 3.1
Use the formula for the probability of a binomial distribution to solve the problem.
Step 3.2
Find the value of .
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.
Step 3.2.3.1
Simplify the numerator.
Step 3.2.3.1.1
Expand to .
Step 3.2.3.1.2
Multiply by .
Step 3.2.3.2
Simplify the denominator.
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.
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 .