Finite Math Examples

$n = 8$ , $x = 1$ , $p = 0.75$

Step 1

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

$p (x) = {}_{8}C_{1} \cdot p^{x} \cdot q^{n - x}$

Step 2

Find the value of ${}_{8}C_{1}$ .

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Step 2.1

Find the number of possible unordered combinations when $r$ items are selected from $n$ available items.

${}_{8}C_{1} = {}_{n}C_{r} = \frac{n!}{(r)! (n - r)!}$

Step 2.2

Fill in the known values.

$\frac{(8)!}{(1)! (8 - 1)!}$

Step 2.3

Simplify.

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Step 2.3.1

Subtract $1$ from $8$ .

$\frac{(8)!}{(1)! (7)!}$

Step 2.3.2

Rewrite $(8)!$ as $8 \cdot 7!$ .

$\frac{8 \cdot 7!}{(1)! (7)!}$

Step 2.3.3

Cancel the common factor of $7!$ .

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Step 2.3.3.1

Cancel the common factor.

$\frac{8 \cdot 7!}{(1)! (7)!}$

Step 2.3.3.2

Rewrite the expression.

$\frac{8}{(1)!}$

Step 2.3.4

Expand $(1)!$ to $1$ .

$\frac{8}{1}$

Step 2.3.5

Divide $8$ by $1$ .

$8$

Step 3

Fill the known values into the equation.

$8 \cdot (0.75) \cdot {(1 - 0.75)}^{8 - 1}$

Step 4

Simplify the result.

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Step 4.1

Evaluate the exponent.

$8 \cdot 0.75 \cdot {(1 - 0.75)}^{8 - 1}$

Step 4.2

Multiply $8$ by $0.75$ .

$6 \cdot {(1 - 0.75)}^{8 - 1}$

Step 4.3

Subtract $0.75$ from $1$ .

$6 \cdot {0.25}^{8 - 1}$

Step 4.4

Subtract $1$ from $8$ .

$6 \cdot {0.25}^{7}$

Step 4.5

Raise $0.25$ to the power of $7$ .

$6 \cdot 0.00006103$

Step 4.6

Multiply $6$ by $0.00006103$ .

$0.00036621$