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# 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. The two-way table summarizes the survey data. begin{array}{c|c}& 4th grade & 5th grade & 6th grade &Total hline Grades &49&50&69&168 text{Athletic} &24&36&38&98 text{Popular} &19&22&28&69 hline text{Total} & 92 & 108 & 135 &335 end{array} Suppose we select one of these students at random. What's the probability of each of the following? The student is a sixth-grader or rated good grades as Important. # 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. The two-way table summarizes the survey data. begin{array}{c|c}& 4th grade & 5th grade & 6th grade &Total hline Grades &49&50&69&168 text{Athletic} &24&36&38&98 text{Popular} &19&22&28&69 hline text{Total} & 92 & 108 & 135 &335 end{array} Suppose we select one of these students at random. What's the probability of each of the following? The student is a sixth-grader or rated good grades as Important.

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Two-way tables asked 2021-01-27
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. The two-way table summarizes the survey data.
$$\begin{array}{c|c}& 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ \text{Athletic} &24&36&38&98\\ \text{Popular}\ &19&22&28&69\\ \hline \text{Total} & 92 & 108 & 135 &335 \end{array}$$
Suppose we select one of these students at random. What's the probability of each of the following? The student is a sixth-grader or rated good grades as Important.

## Answers (1) 2021-01-28
Given:
$$\begin{array}{c|c}& 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ \text{Athletic} &24&36&38&98\\ \text{Popular}\ &19&22&28&69\\ \hline \text{Total} & 92 & 108 & 135 &335 \end{array}$$
The table contains data of 335 students, which is given in the bottom right corner of the given table.
$$\text{# of possible outcomes} = 335$$
All students who are 6th grades and rated good grades as important are given in the row "6th grade” or in the column ”Grades” of the given table. Adding all corresponding counts, we then note that this corresponds with 49+50+69+38 +28=211 students who are 6th graders or rated good grades as important.
$$\text{# of favorable outcomes} = 234$$
The probability is the number of favorable outcomes divided by the number of possible outcomes:
$$P(\text{ 6th grade or Grades})=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}$$
$$=\frac{234}{335}$$
$$\approx 0.6985$$
$$=69.85\%$$

### Relevant Questions asked 2021-02-09
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. The two-way table summarizes the survey data.
$$\begin{array}{c|c} & 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ Athletic &24&36&38&98\\ Popular\ &19&22&28&69\\ \hline Total & 92 & 108 & 135 &335 \end{array}$$
Suppose we select one of these students at random. What's the probability of each of the following? The student is not a sixth-grader and did not rate good grades as important. asked 2020-10-19

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.

$$\begin{array} {|c|} & Grade \ Most important & \begin{array}{l|c|c|c|c} & \begin{array}{c} 4 \mathrm{th} \ grade \end{array} & \begin{array}{c} 5 \mathrm{th} \ \text { grade } \end{array} & \begin{array}{c} 6 \mathrm{th} \ grade \end{array} & Total \\ \hline Grades & 49 & 50 & 69 & 168 \\ \hline Athletic & 24 & 36 & 38 & 98 \\ \hline Popular & 19 & 22 & 28 & 69 \\ \hline Total & 92 & 108 & 135 & 335 \end{array} \ \end{array}$$

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? asked 2020-11-14

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. The two-way table summarizes the survey data.

$$Grade\ Most\ important\begin{array}{l|c|c|c|c} & 4 \mathrm{th} & 5 \mathrm{th} & 6 \mathrm{th} & \text { Total } \\ \hline Grades & 49 & 50 & 69 & 168 \\ \hline Athletic & 24 & 36 & 38 & 98 \\ \hline Popular & 19 & 22 & 28 & 69 \\ \hline Total & 92 & 108 & 135 & 335 \end{array}$$

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Suppose one adult is selected at random from these 1950 adults. Find the following probablity.
Round your answer to three decimal places.
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