Statistics Examples

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

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

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

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

Tap for more steps...

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

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

Fill in the known values.

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

Simplify.

Tap for more steps...

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

Tap for more steps...

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

Tap for more steps...

Subtract $4$ from $4$ .

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

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

$\frac{1}{1}$

Divide $1$ by $1$ .

$1$

Fill the known values into the equation.

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

Simplify the result.

Tap for more steps...

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

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

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

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

Subtract $0.8$ from $1$ .

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

Subtract $4$ from $4$ .

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

Anything raised to $0$ is $1$ .

$0.4096 \cdot 1$

Multiply $0.4096$ by $1$ .

$0.4096$

Enter YOUR Problem