 # Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Tammy Todd 2020-10-19 Answered

Researchers carried out a survey of fourth-, fifth-, and sixth-grade students in Michigan. Students were asked whether good grades, athletic ability, or being popular was most important to them. This two-way table summarizes the survey data.

Suppose we select one of these students at random. What's the probability that: The student is a sixth grader or a student who rated good grades as important?

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Definitions: Completed rule $P\left({A}^{c}\right)=P\left(\mathrm{¬}A\right)=1-P\left(A\right)$ General addition rule for any two events:$P\left(AorB\right)=P\left(A\right)+P\left(B\right)-P\left(AandB\right)$

Solution

S = Sixth grader G = Grades We note that 135 of the 335 people in the table are 6th grades, because 135 is mentioned in the row ” Total” and in the column ”6th grade” of the given table. The probability is the number of favorable outcomes divided by the number of possible outcomes: We note that 168 of the 335 people in the table rated good grades as important, because 168 is mentioned in the row ” Grades” and in the column ”Total” of the given table. We note that 69 of the 335 people in the table are 6th graders who rated good grades as important, because 69 is mentioned in the row ” Grades” and in the column ”6th gradel” of the given table. $P\left(G\right)=\frac{\mathrm{#}\text{of favor about comes}}{\mathrm{#}\text{of possible out comes}}=\frac{69}{335}$ Use the general addition rule: $P\left(S\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}G\right)=P\left(S\right)+P\left(G\right)-P\left(S\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}G\right)$
$=\frac{135}{335}+\frac{168}{335}-\frac{69}{335}$
$=\frac{135+168-69}{335}$
$=\frac{234}{335}$
$\approx 0.6985$
$=69.85\mathrm{%}$