Question

a quality control inspector is checking a sample of light bulbs. the table summarizes her results. if one of the light bulbs is selected at random, find the probability that the light bulb is defective, given that it is a 50 or 100 watt bulb.

\

$$\begin{tabular}{|c|c|c|c|} \\hline wattage & good & defective & total \\\\ \\hline 20 & 86 & 5 & 91 \\\\ 50 & 85 & 12 & 97 \\\\ 100 & 99 & 15 & 114 \\\\ total & 270 & 32 & 302 \\\\ \\hline \\end{tabular}$$

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

Explanation:

Identify the given condition and target event

Using the Conditional Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the size of the restricted sample space

Using the Conditional Probability knowledge point

$$
LATEXBLOCK1
$$

Calculate the number of favorable outcomes

Using the Conditional Probability knowledge point

$$
LATEXBLOCK2
$$

Compute the conditional probability

Using the Conditional Probability knowledge point

$$ P(D \mid C) = \frac{N(D \cap C)}{N(C)} = \frac{27}{211} $$

Simplify the resulting fraction

Using the Fraction Simplification knowledge point

$$
LATEXBLOCK3
$$

Answer:

A quality control inspector is checking a sample of light bulbs. The table summarizes her results. If one of the light bulbs is selected at random, find the probability that the light bulb is defective, given that it is a 50 or 100 watt bulb.

The probability is <blank>\(\frac{27}{211}\)</blank>
(Simplify your answer. Type an integer or a fraction.)