1) A local high school takes pride in the fact that $$ 72 \% $$ of its students participate in after school activities. 1) If 2 students are randomly selected, what is the probability that at least 1 of the chose students participates in after school activities? ()) Write your answer as a decimal rounded to the nearest thousandth.

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UpStudy AI · Accepted Answer

To determine the probability that at least one of the two randomly selected students participates in after school activities, follow these steps:

1. **Determine the probability of a single event:**
   - **Probability a student participates:** $$ P(\text{participate}) = 72\% = 0.72 $$
   - **Probability a student does not participate:** $$ P(\text{not participate}) = 1 - 0.72 = 0.28 $$

2. **Calculate the probability that neither of the two students participates:**
   $$
   P(\text{neither participates}) = P(\text{not participate}) \times P(\text{not participate}) = 0.28 \times 0.28 = 0.0784
   $$

3. **Find the probability that at least one student participates:**
   $$
   P(\text{at least one participates}) = 1 - P(\text{neither participates}) = 1 - 0.0784 = 0.9216
   $$

4. **Round the answer to the nearest thousandth:**
   $$
   0.9216 \approx 0.922
   $$

**Final Answer:**  
The probability is **0.922**.
The probability that at least one of the two selected students participates in after school activities is **0.922**.

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