Determine if the first event of each experiment is independent or dependent: Identifying independent events given descriptions of experiments \begin{tabular}{|c|c|c|c|} \hline Experiment & Events & Independent & Dependent \\ \hline \multirow[t]{2}{*}{\begin{tabular}{l} A box contains tiles labeled A through $\mathrm{Z}$. A tile is randomly \\ chosen from the box and set aside. Then another random \\ selection is made from the remaining tiles. \end{tabular}} & \begin{tabular}{l} Event $A$ : The first \\ selection is a tile labeled \\ with a "B". \end{tabular} & \multirow{2}{*}{0} & \multirow{2}{*}{0} \\ \hline & \begin{tabular}{l} Event $B$ : The second \\ selection is a tile labeled \\ with a " $Y$ ". \end{tabular} & & \\ \hline \multirow[t]{2}{*}{\begin{tabular}{l} A paper clip is randomly selected from a container with black \\ clips and white clips and thrown away. Then another random \\ selection is made from the remaining clips. \end{tabular}} & \begin{tabular}{l} Event $A$ : The first \\ selection is a black \\ paper clip. \end{tabular} & \multirow[b]{2}{*}{0} & \multirow[b]{2}{*}{0} \\ \hline & \begin{tabular}{l} Event $B$ : The second \\ selection is a white \\ paper clip. \end{tabular} & & \\ \hline \multirow[t]{2}{*}{ A spinner with slices numbered 1 through 9 is spun twice. } & \begin{tabular}{l} Event A: The first spin \\ lands on 8. \end{tabular} & \multirow[b]{2}{*}{0} & \multirow[b]{2}{*}{0} \\ \hline & \begin{tabular}{l} Event B: The second \\ spin lands on 4. \end{tabular} & & \\ \hline \end{tabular} Explanation Check
Solution
Step 1 ：The question asks to determine if the first event of each experiment is independent or dependent.
Step 2 ：In the first experiment, the first event is choosing a tile labeled with a 'B'. The second event is choosing a tile labeled with a 'Y'. These events are dependent because the outcome of the first event affects the outcome of the second event. After the first tile is chosen and set aside, there are fewer tiles left in the box, which changes the probabilities of the remaining tiles being chosen.
Step 3 ：In the second experiment, the first event is choosing a black paper clip. The second event is choosing a white paper clip. These events are also dependent because the outcome of the first event affects the outcome of the second event. After the first paper clip is chosen and thrown away, there are fewer paper clips left in the container, which changes the probabilities of the remaining paper clips being chosen.
Step 4 ：In the third experiment, the first event is the first spin landing on 8. The second event is the second spin landing on 4. These events are independent because the outcome of the first event does not affect the outcome of the second event. The spinner has the same probabilities for each spin, regardless of the outcome of previous spins.
Step 5 ：Final Answer: \(\boxed{\text{The first event of the first experiment is dependent.}}\)
Step 6 ：\(\boxed{\text{The first event of the second experiment is dependent.}}\)
Step 7 ：\(\boxed{\text{The first event of the third experiment is independent.}}\)
