# Statistics Examples

, ,

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

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

Subtract from .

Step 3.2.3.2

Rewrite as .

Step 3.2.3.3

Cancel the common factor of .

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.

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

Step 4.1

Use the formula for the probability of a binomial distribution to solve the problem.

Step 4.2

Find the value of .

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.

Step 4.2.3.1

Subtract from .

Step 4.2.3.2

Rewrite as .

Step 4.2.3.3

Cancel the common factor of .

Step 4.2.3.3.1

Cancel the common factor.

Step 4.2.3.3.2

Rewrite the expression.

Step 4.2.3.4

Expand to .

Step 4.2.3.5

Divide by .

Step 4.3

Fill the known values into the equation.

Step 4.4

Simplify the result.

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

Evaluate the exponent.

Step 4.4.6

Multiply by .

Step 5

Step 5.1

Use the formula for the probability of a binomial distribution to solve the problem.

Step 5.2

Find the value of .

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.

Step 5.2.3.1

Cancel the common factor of .

Step 5.2.3.1.1

Cancel the common factor.

Step 5.2.3.1.2

Rewrite the expression.

Step 5.2.3.2

Simplify the denominator.

Step 5.2.3.2.1

Subtract from .

Step 5.2.3.2.2

Expand to .

Step 5.2.3.3

Divide by .

Step 5.3

Fill the known values into the equation.

Step 5.4

Simplify the result.

Step 5.4.1

Multiply by .

Step 5.4.2

Raise to the power of .

Step 5.4.3

Subtract from .

Step 5.4.4

Subtract from .

Step 5.4.5

Anything raised to is .

Step 5.4.6

Multiply by .

Step 6

Step 6.1

Add and .

Step 6.2

Add and .