Question

a quality control inspector is checking a sample of lightbulbs for defects. the table summarizes the results. if one of these lightbulbs is selected at random, find the probability that the lightbulb is good, given that it is 100 watts.

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$$\begin{tabular}{|r|r|r|r|} \\hline wattage & good & defective & total \\\\ \\hline 20 & 66 & 6 & 72 \\\\ 50 & 56 & 12 & 68 \\\\ 100 & 84 & 6 & 90 \\\\ total & 206 & 24 & 230 \\\\ \\hline \\end{tabular}$$

the probability is \\\\
(simplify your answer. type an integer or a fraction.)

Explanation:

Identify the given condition

Using the Conditional Probability knowledge point

$$ \text{Given Condition: The lightbulb is 100 watts.} $$

$$ \text{Total number of 100-watt lightbulbs} = 90 $$

Identify the favorable outcomes

Using the Conditional Probability knowledge point

$$ \text{Favorable Event: The lightbulb is good AND is 100 watts.} $$

$$ \text{Number of good 100-watt lightbulbs} = 84 $$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(\text{Good} \mid \text{100 Watts}) = \frac{84}{90} $$

Simplify the fraction

Using the Fraction Simplification knowledge point

$$ \frac{84}{90} = \frac{84 \div 6}{90 \div 6} = \frac{14}{15} $$

Answer:

The probability is <blank>\(\frac{14}{15}\)</blank>.
(Simplify your answer. Type an integer or a fraction.)