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 not 20 watts.

\

$$\begin{tabular}{|r|r|r|r|} \\hline wattage & good & defective & total \\\\ \\hline 20 & 96 & 10 & 106 \\\\ 50 & 78 & 12 & 90 \\\\ 100 & 70 & 8 & 78 \\\\ total & 244 & 30 & 274 \\\\ \\hline \\end{tabular}$$

the probability is .
(type an integer or a simplified fraction.)

Explanation:

Define the given events

Using the Conditional Probability knowledge point
Let \(G\) be the event that the lightbulb is good.
Let \(N\) be the event that the lightbulb is not 20 watts.

Determine the size of the reduced sample space

Using the Conditional Probability knowledge point

$$
LATEXBLOCK0
$$

Determine the number of favorable outcomes

Using the Conditional Probability knowledge point

$$
LATEXBLOCK1
$$

Calculate the conditional probability

Using the Conditional Probability knowledge point

$$ P(G \mid N) = \frac{n(G \cap N)}{n(N)} = \frac{148}{168} $$

Simplify the resulting fraction

Using the Fraction Simplification knowledge point

$$ \frac{148}{168} = \frac{148 \div 4}{168 \div 4} = \frac{37}{42} $$

Answer:

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 not 20 watts.

The probability is <blank>\(\frac{37}{42}\)</blank>.
(Type an integer or a simplified fraction.)