实验概率与理论概率
Experimental vs Theoretical
重复进行概率实验,比较实验(相对频率)结果与理论预测;理解并说明:随着试验次数增加,实验概率会逐渐趋近理论概率,而试验次数较少时,结果可能会有很大差异。
Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results
学习证据 / Evidence
- 掷骰子60次,比较每个点数出现的实验频率与理论预期(每个点数出现10次)。
- 解释为什么实验结果不会与理论预测完全一致,但随着试验次数增加,结果会越来越接近理论预测。
- 预测如果实验重复600次而不是60次,结果会怎样。
- Roll a die 60 times and compare experimental frequencies with the expected 10 per number
- Explain why experimental results don't exactly match theoretical predictions but get closer with more trials
- Predict what would happen if the experiment were repeated 600 times instead of 60
评估问题 / Assessment
如果{{name}}掷一枚硬币10次,有7次正面朝上,{{name}}是否明白为什么这并不意味着正面朝上“更有可能”,而且掷的次数越多,结果就会越接近50:50?
If {{name}} flips a coin 10 times and gets 7 heads, do they understand why this doesn't mean heads is "more likely" — and that the more times you flip, the closer the results get to 50:50?