Finite Math Examples

x = 2

$x = 2$ ,

n = 3

$n = 3$ ,

p = 0.2

$p = 0.2$

Step 1

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

$p (x) = {}_{3}C_{2} \cdot p^{x} \cdot q^{n - x}$

Step 2

Find the value of

${}_{3}C_{2}$ .

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Step 2.1

Find the number of possible unordered combinations when

$r$ items are selected from

$n$ available items.

${}_{3}C_{2} = {}_{n}C_{r} = \frac{n!}{(r)! (n - r)!}$

Step 2.2

Fill in the known values.

$\frac{(3)!}{(2)! (3 - 2)!}$

Step 2.3

Simplify.

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Step 2.3.1

Subtract

$2$ from

$3$ .

$\frac{(3)!}{(2)! (1)!}$

Step 2.3.2

Rewrite

$(3)!$ as

$3 \cdot 2!$ .

$\frac{3 \cdot 2!}{(2)! (1)!}$

Step 2.3.3

Cancel the common factor of

$2!$ .

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Step 2.3.3.1

Cancel the common factor.

$\frac{3 \cdot 2!}{(2)! (1)!}$

Step 2.3.3.2

Rewrite the expression.

$\frac{3}{(1)!}$

Step 2.3.4

Expand

$(1)!$ to

$1$ .

$\frac{3}{1}$

Step 2.3.5

Divide

$3$ by

$1$ .

$3$

Step 3

Fill the known values into the equation.

$3 \cdot {(0.2)}^{2} \cdot {(1 - 0.2)}^{3 - 2}$

Step 4

Simplify the result.

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Step 4.1

Raise

$0.2$ to the power of

$2$ .

$3 \cdot 0.04 \cdot {(1 - 0.2)}^{3 - 2}$

Step 4.2

Multiply

$3$ by

$0.04$ .

$0.12 \cdot {(1 - 0.2)}^{3 - 2}$

Step 4.3

Subtract

$0.2$ from

$1$ .

$0.12 \cdot {0.8}^{3 - 2}$

Step 4.4

Subtract

$2$ from

$3$ .

$0.12 \cdot {0.8}^{1}$

Step 4.5

Evaluate the exponent.

$0.12 \cdot 0.8$

Step 4.6

Multiply

$0.12$ by

$0.8$ .

$0.096$

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