Question

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

\\c_{0}^{6} (0.05)^{0} (0.95)^{6}\\

you may need to use the appropriate appendix table to answer this question.

Explanation:

Identify the components of the expression

Using the Binomial Probability Distribution knowledge point
The given expression is:

$$ C_{0}^{6} (0.05)^{0} (0.95)^{6} $$

This represents the probability of obtaining exactly \(k = 0\) successes in \(n = 6\) independent trials, where the probability of success on a single trial is \(p = 0.05\) and the probability of failure is \(q = 0.95\).

Calculate the combination term

Using the Binomial Probability Distribution knowledge point

$$ C_{0}^{6} = \frac{6!}{0!(6-0)!} = 1 $$

Evaluate the exponential terms

Using the Binomial Probability Distribution knowledge point

$$ (0.05)^{0} = 1 $$

$$ (0.95)^{6} \approx 0.73509189 $$

Multiply the terms and round

Using the Binomial Probability Distribution knowledge point

$$ 1 \times 1 \times 0.73509189 \approx 0.73509189 $$

Rounding to three decimal places:

$$ 0.735 $$

Answer:

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

$$ C_{0}^{6} (0.05)^{0} (0.95)^{6} $$

<blank>0.735</blank>