Question

refer to the table, which contains information about 36 jars of salsa available at a particular food pantry. if a jar is randomly selected, determine the probability that the salsa is not brand c.

\

$$\begin{array}{lcccc} \\text{brand} & \\text{mild} & \\text{medium} & \\text{hot} & \\text{total} \\\\ \\text{a} & 6 & 1 & 3 & 10 \\\\ \\text{b} & 4 & 2 & 5 & 11 \\\\ \\text{c} & 0 & 7 & 8 & 15 \\\\ \\text{total} & 10 & 10 & 16 & 36 \\end{array}$$

if a jar is randomly selected, the probability that the salsa is not brand c is .
(simplify your answer.)

Explanation:

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<reasoning>

Identify total outcomes and favorable outcomes

Using the Complementary Events knowledge point
\[

$$\begin{aligned} &\text{Total number of jars } (N) = 36\\ &\text{Number of Brand C jars } (n_C) = 15\\ &\text{Number of jars not Brand C } (n_{\text{not } C}) = N - n_C = 36 - 15 = 21 \end{aligned}$$

\]

Calculate the probability

Using the Complementary Events knowledge point
\[
P(\text{not Brand C}) = \frac{n_{\text{not } C}}{N} = \frac{21}{36}
\]

Simplify the fraction

Using the Fraction Simplification knowledge point
\[
\frac{21}{36} = \frac{21 \div 3}{36 \div 3} = \frac{7}{12}
\]
</reasoning>

<answer>
If a jar is randomly selected, the probability that the salsa is not Brand C is <blank>\(\frac{7}{12}\)</blank>.
</answer>

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Answer:

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<reasoning>

Identify total outcomes and favorable outcomes

Using the Complementary Events knowledge point
\[

$$\begin{aligned} &\text{Total number of jars } (N) = 36\\ &\text{Number of Brand C jars } (n_C) = 15\\ &\text{Number of jars not Brand C } (n_{\text{not } C}) = N - n_C = 36 - 15 = 21 \end{aligned}$$

\]

Calculate the probability

Using the Complementary Events knowledge point
\[
P(\text{not Brand C}) = \frac{n_{\text{not } C}}{N} = \frac{21}{36}
\]

Simplify the fraction

Using the Fraction Simplification knowledge point
\[
\frac{21}{36} = \frac{21 \div 3}{36 \div 3} = \frac{7}{12}
\]
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If a jar is randomly selected, the probability that the salsa is not Brand C is <blank>\(\frac{7}{12}\)</blank>.
</answer>

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