To determine the chances that a sixth grader in the survey plays both basketball and soccer, we need to evaluate the combined probability of these two independent events occurring together. Here’s the step-by-step solution:
1. Understand the Probabilities:
- The probability that a sixth grader plays basketball is given as [tex]\( 25\% \)[/tex].
- The probability that a sixth grader plays soccer is given as [tex]\( 17\% \)[/tex].
2. Convert Percentages to Probabilities:
- [tex]\( 25\% \)[/tex] as a probability is [tex]\( 0.25 \)[/tex].
- [tex]\( 17\% \)[/tex] as a probability is [tex]\( 0.17 \)[/tex].
3. Calculate the Combined Probability:
- Since the events (playing basketball and playing soccer) are independent, the combined probability is found by multiplying the two individual probabilities.
[tex]\[
\text{Combined Probability} = 0.25 \times 0.17
\][/tex]
4. Perform the Multiplication:
- Multiply [tex]\( 0.25 \)[/tex] by [tex]\( 0.17 \)[/tex]:
[tex]\[
0.25 \times 0.17 = 0.0425
\][/tex]
5. Convert the Combined Probability to a Percentage:
- To express the combined probability as a percentage, multiply by [tex]\( 100 \)[/tex]:
[tex]\[
0.0425 \times 100 = 4.25\%
\][/tex]
So, the chances that a sixth grader plays both basketball and soccer is [tex]\( 4.25\% \)[/tex].
Considering the simulation options provided:
- The best method to simulate this would be to spin and roll 90 times and count the number of times you get a specific outcome that satisfies both conditions (e.g., spin a number less than 3 and roll a 4). This will help in understanding how often both events happen together based on the defined conditions. Thus, out of all options given, the method "Spin and roll 90 times & spin less than 3 AND roll a 4" aligns with approximating the desired event probability.
