Question

evaluate the binomial probability. (round your answer to three decimal places.)

\\(c_{5}^{1} (0.3)^{1} (0.7)^{4}\\)

Explanation:

Identify the expression

Using the Binomial Probability Distribution knowledge point
The given image is upside down. Let's rotate and transcribe the expression:

$$ C_{5}^{1} (0.3)^{1} (0.7)^{4} $$

The question asks to: "Evaluate the binomial probability. (Round your answer to three decimal places.)"

Calculate the combination

Using the Binomial Probability Distribution knowledge point

$$ C_{5}^{1} = \frac{5!}{1!(5-1)!} = 5 $$

Calculate the exponential terms

Using the Binomial Probability Distribution knowledge point

$$ (0.3)^{1} = 0.3 $$

$$ (0.7)^{4} = 0.2401 $$

Multiply the terms together

Using the Binomial Probability Distribution knowledge point

$$ \text{Probability} = 5 \times 0.3 \times 0.2401 = 1.5 \times 0.2401 = 0.36015 $$

Round to three decimal places

Using the Binomial Probability Distribution knowledge point

$$ 0.36015 \approx 0.360 $$

Answer:

Evaluate the binomial probability. (Round your answer to three decimal places.)

\(C_{5}^{1} (0.3)^{1} (0.7)^{4} =\) <blank>0.360</blank>