Finite Math Examples Statistical Distributions

Find the Probability of the Binomial Event

$x = 4$ , $n = 4$ , $p = 0.8$

Step 1

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

$p (x) = {}_{4}C_{4} \cdot p^{x} \cdot q^{n - x}$

Step 2

Find the value of ${}_{4}C_{4}$ .

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Step 2.1

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

${}_{4}C_{4} = {}_{n}C_{r} = \frac{n!}{(r)! (n - r)!}$

Step 2.2

Fill in the known values.

$\frac{(4)!}{(4)! (4 - 4)!}$

Step 2.3

Simplify.

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Step 2.3.1

Cancel the common factor of $(4)!$ .

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Step 2.3.1.1

Cancel the common factor.

$\frac{(4)!}{(4)! (4 - 4)!}$

Step 2.3.1.2

Rewrite the expression.

$\frac{1}{(4 - 4)!}$

Step 2.3.2

Simplify the denominator.

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Step 2.3.2.1

Subtract $4$ from $4$ .

$\frac{1}{(0)!}$

Step 2.3.2.2

Expand $(0)!$ to $1$ .

$\frac{1}{1}$

Step 2.3.3

Divide $1$ by $1$ .

$1$

Step 3

Fill the known values into the equation.

$1 \cdot {(0.8)}^{4} \cdot {(1 - 0.8)}^{4 - 4}$

Step 4

Simplify the result.

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Step 4.1

Multiply ${(0.8)}^{4}$ by $1$ .

${(0.8)}^{4} \cdot {(1 - 0.8)}^{4 - 4}$

Step 4.2

Raise $0.8$ to the power of $4$ .

$0.4096 \cdot {(1 - 0.8)}^{4 - 4}$

Step 4.3

Subtract $0.8$ from $1$ .

$0.4096 \cdot {0.2}^{4 - 4}$

Step 4.4

Subtract $4$ from $4$ .

$0.4096 \cdot {0.2}^{0}$

Step 4.5

Anything raised to $0$ is $1$ .

$0.4096 \cdot 1$

Step 4.6

Multiply $0.4096$ by $1$ .

$0.4096$

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Statistical Distributions

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Statistical Distributions

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