Statistics Examples

$x = 2$ , $n = 3$ , $p = 0.2$

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

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

Find the value of ${}_{3}C_{2}$ .

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

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

Fill in the known values.

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

Simplify.

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Subtract $2$ from $3$ .

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

Rewrite $(3)!$ as $3 \cdot 2!$ .

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

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

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

Rewrite the expression.

$\frac{3}{1!}$

Expand $1!$ to $1$ .

$\frac{3}{1}$

Divide $3$ by $1$ .

$3$

Fill the known values into the equation.

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

Simplify the result.

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Remove parentheses around $0.2$ .

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

Raise $0.2$ to the power of $2$ .

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

Multiply $3$ by $0.04$ .

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

Subtract $0.2$ from $1$ .

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

Subtract $2$ from $3$ .

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

Remove parentheses around $0.8$ .

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

Evaluate the exponent.

$0.12 \cdot 0.8$

Multiply $0.12$ by $0.8$ .

$0.096$

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