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.

Question
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:
\(P(\text{ 6th grade or Grades})=\frac{\text{# of favorable outcomes}}{\text{# of possible outcomes}}\)
\(=\frac{234}{335}\)
\(\approx 0.6985\)
\(=69.85\%\)
0

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