Question

# The two-way table summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level. \text{Grade}\ \te

Random variables
The two-way table summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level. \text{Grade}\ \text{Eat in cafeteria} \begin{array}{l|r|r|r|r|r} & 9 \mathrm{th} & 10 \mathrm{th} & 11 \mathrm{th} & 12 \mathrm{th} & \text { Total } \ \hline \text { Yes } & 130 & 175 & 122 & 68 & 495 \ \hline \text { No } & 18 & 34 & 88 & 170 & 310 \ \hline \text { Total } & 148 & 209 & 210 & 238 & 805 \end{array} If you choose a student at random, what is the probability that the student eats regularly in the cafeteria and is not a 10th-grader?

2021-05-29
Given:
9th 10th 11th 12th | Total
Yes 130 175 122 68 | 495
No 18 34 88 170 | 310
Total 148 209 210 238 | 805
The table contains 805 students in total (which is given in the bottom right, corner of the table), while 130+122+68 = 320 of the 805 students eat regularly in the cafeteria and is not a 10th graders (since 130 is mentioned in the row” Yes” and in the column "9th? of the given table, 122 is mentioned in the row” Yes” and in the column” 11th” ofthe given table, 68 is mentioned in the row ” Yes” and in the column ”12th” of the given table).
The probability is the number of favorable outcomes divided by the number of possible outcomes:
P(Yes and not 10th)=# of favorable outcomes/# of possible outcomes=$$\displaystyle\frac{{320}}{{805}}=\frac{{64}}{{161}}\sim{0.3975}\sim{39.75}\%$$