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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, o

Two-way tables
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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.

Expert Answers (1)

2021-02-10
Given
\(\begin{array}{c|c} & 4th\ grade & 5th\ grade & 6th\ grade &Total \\ \hline Grades &49&50&69&168\\ Athletic &24&36&38&98\\ Popular\ &19&22&28&69\\ \hline Total & 92 & 108 & 135 &335 \end{array}\)
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 not sixth-graders and did not rate good grades as important are given in the rows "4th grade” and "5th grade”, while they are also given in the columns” Athletic” and”Popular”. Adding all corresponding counts, we then note that this corresponds with 24+36+19+22=124 students who are not sixth graders and did not rate good grades as important.
\(\# \text{ of favorable outcomes}=101\)
The probability is the number of favorable outcomes divided by the number of possible outcomes:
\(P(\text{Not sixth grades and no grades})=\frac{\# \text{ of favorable outcomes}}{\#\text{ of possible outcomes}}=\frac{101}{335}\)
\(\approx0.3015\)
\(=30.15\%\)
Answer: \(\frac{101}{335}\approx0.3015=30.15\%\)
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