A special deck of cards has 5 red tards, and 4 purple cards. The red cards are numbered 1, 2, 3, 4, and 5 . . The purple cards are numbered \( 1,2,3 \), and 4 . The cards are well shuffled and you randomly draw one card. \( \mathrm{R}= \) card drawn is red \( \mathrm{E}= \) card drawn is even-numbered a. How many elements are there in the sample space? b. \( \mathrm{P}(\mathrm{E})=\square \) Round your answer to two decimal places. Hint: Sample Space and Probability Video on Probability

**Step 1. Count the total number of cards** - Number of red cards: \(5\) - Number of purple cards: \(4\) The sample space consists of all the cards: \[ \text{Total cards} = 5 + 4 = 9 \] Thus, the total number of elements in the sample space is **9**. --- **Step 2. Identify the even-numbered cards** We need to find how many cards have an even number. - **Red cards:** The red cards are numbered \(1, 2, 3, 4,\) and \(5\). The even numbers among these are \(2\) and \(4\). So, there are \(2\) even-numbered red cards. - **Purple cards:** The purple cards are numbered \(1, 2, 3,\) and \(4\). The even numbers among these are \(2\) and \(4\). So, there are \(2\) even-numbered purple cards. Adding these together, we have: \[ \text{Total even-numbered cards} = 2 + 2 = 4 \] --- **Step 3. Calculate the probability \( \mathrm{P}(E) \)** The probability of drawing an even-numbered card is: \[ \mathrm{P}(E) = \frac{\text{Number of even cards}}{\text{Total number of cards}} = \frac{4}{9} \] Rounded to two decimal places: \[ \frac{4}{9} \approx 0.44 \] --- **Final Answers:** a. \(9\) b. \( \mathrm{P}(E) \approx 0.44 \)