Problem
For all probabilities, show work, round decimal answers to 3 decimal places and percent answers to 1 decimal. \begin{tabular}{|c|c|c|c|c|} \cline { 2 - 5 } \multicolumn{1}{c|}{} & Blue & Red & Green & Total \\ \hline Circle & 10 & 4 & 9 & 23 \\ \hline Triangle & 3 & 2 & 7 & 12 \\ \hline Total & 13 & 6 & 16 & 35 \\ \hline \end{tabular} 3. A bag contains two shapes, and each shape can be one of three colors. The two-way table above shows the frequency of each shape. What is the probability of randomly choosing a green shape? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ & & \\ \hline \end{tabular} What is the probability of randomly choosing a red shape and it is a circle? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ \hline \end{tabular} What is the probability of randomly choosing a blue or red shape? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ \hline \end{tabular} What is the probability of randomly choosing an item that is red or a triangle? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ & & \\ \hline \end{tabular} Assuming the item you select is green, what is the probability it is a circle? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ \hline \end{tabular} What is the probability of choosing a blue circle, returning it, and then choosing a blue triangle? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ & & \\ \hline \end{tabular} If you chose two objects in a row and did not return either of them, what is the probability they are both blue? \begin{tabular}{|l|l|l|} \hline Fraction & Decimal (3 places) & Percent \\ \hline & & \\ & & \\ \hline \end{tabular}
Solution
Step 1 ：\( P(\text{Green shape}) = \frac{16}{35} \) \( \approx 0.457 \) \( \approx 45.7\% \)
Step 2 ：\( P(\text{Red circle}) = \frac{4}{35} \) \( \approx 0.114 \) \( \approx 11.4\% \)
Step 3 ：\( P(\text{Blue or Red shape}) = \frac{13+6}{35} \) \( \approx 0.543 \) \( \approx 54.3\% \)
Step 4 ：\( P(\text{Red or Triangle}) = \frac{6+12}{35} \) \( \approx 0.514 \) \( \approx 51.4\% \)
Step 5 ：\( P(\text{Circle} | \text{Green}) = \frac{9}{16} \) \( \approx 0.562 \) \( \approx 56.2\% \)
Step 6 ：\( P(\text{Blue circle, return, Blue triangle}) = \frac{10}{35} \cdot \frac{3}{35} \) \( \approx 0.008 \) \( \approx 0.8\% \)
Step 7 ：\( P(\text{Both blue, no return}) = \frac{10}{35} \cdot \frac{9}{34} \) \( \approx 0.075 \) \( \approx 7.5\% \)
