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We have been given a two-way table that summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

We need to find out the probability that the student eats regularly in the cafeteria and is not a $10th鈥�$grader.

Let A$=$Student who eats regularly in the cafeteria and is a $10th鈥�$grader.

Let B$=$Student who eats regularly in the cafeteria and is not a $10th鈥�$grader.

$$\begin{gathered} P\left(B\right)=\frac{no.offavourableoutcomes}{no.ofpossibleoutcomes} \\ =\frac{320}{805}=\frac{64}{161}鈮�0.3975=39.75\% \end{gathered}$$

We have been given a two-way table that summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

We need to find out the probability that the student eats regularly in the cafeteria and is a $10th鈥�$grader.

Let A$=$Student who eats regularly in the cafeteria and is a $10th鈥�$grader.

Let B $=$Student who eats regularly in the cafeteria and is not a $10th鈥�$grader.

$$\begin{gathered} P\left(A\right)=\frac{no.offavourableoutcomes}{no.ofpossibleoutcomes} \\ =\frac{175}{495}=\frac{35}{99}鈮�.3535=35.35\% \end{gathered}$$

We have been given a two-way table that summarizes data on whether students at a certain high school eat regularly in the school cafeteria by grade level.

We need to find out whether the events 鈥�$10th鈥�$grader鈥� and 鈥渆ats regularly in the cafeteria鈥� are independent or not.

Let A$=$Student who eats regularly in the cafeteria and is a $10th鈥�$grader.

$$\begin{gathered} P\left(A\right)=\frac{no.offavourableoutcomes}{no.ofpossibleoutcomes} \\ =\frac{175}{495}=\frac{35}{99}鈮�.3535=35.35\% \end{gathered}$$

Let C$=$Students of $10th鈥�$grade

$$\begin{gathered} P\left(C\right)=\frac{no.offavourableoutcomes}{no.ofpossibleoutcomes} \\ =\frac{209}{805}鈮�0.2596=25.96\% \end{gathered}$$

As shown above,$P\left(A\right)鈮�P\left(C\right)$which implies that the events 鈥�$10th鈥�$grader鈥� and 鈥渆ats regularly in the cafeteria鈥� are not independent