Statistics Examples

$x = 3$ , $n = 4$ , $p = 0.6$

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

$p (x) = {}_{4}C_{3} \cdot p^{x} \cdot q^{n - x}$

Find the value of ${}_{4}C_{3}$ .

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

${}_{4}C_{3} = {}_{n}C_{r} = \frac{n!}{(r)! (n - r)!}$

Fill in the known values.

$\frac{(4)!}{(3)! (4 - 3)!}$

Simplify.

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Subtract $3$ from $4$ .

$\frac{(4)!}{(3)! (1)!}$

Rewrite $(4)!$ as $4 \cdot 3!$ .

$\frac{4 \cdot 3!}{(3)! (1)!}$

Reduce the expression by cancelling the common factors.

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Cancel the common factor.

$\frac{4 \cdot 3!}{(3)! (1)!}$

Rewrite the expression.

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

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

$\frac{4}{1}$

Divide $4$ by $1$ .

$4$

Fill the known values into the equation.

$4 \cdot {(0.6)}^{3} \cdot {(1 - 0.6)}^{4 - 3}$

Simplify the result.

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Raise $0.6$ to the power of $3$ .

$4 \cdot 0.216 \cdot {(1 - 0.6)}^{4 - 3}$

Multiply $4$ by $0.216$ .

$0.864 \cdot {(1 - 0.6)}^{4 - 3}$

Subtract $0.6$ from $1$ .

$0.864 \cdot {(0.4)}^{4 - 3}$

Subtract $3$ from $4$ .

$0.864 \cdot {(0.4)}^{1}$

Evaluate the exponent.

$0.864 \cdot 0.4$

Multiply $0.864$ by $0.4$ .

$0.3456$

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