8. 独立事件与互斥事件

功能简介：通过可视化展示事件的独立性和互斥性，计算相关概率。支持设置事件概率，模拟多次实验，展示事件关系的直观理解，帮助学生区分独立事件和互斥事件的概念。

ArkTS代码：

@Entry
@Component
struct IndependentEvents {
  @State private pA: number = 0.5
  @State private pB: number = 0.5
  @State private trials: number = 1000
  @State private result: string = ''
  @State private eventType: string = ''

  build() {
    Column() {
      Text('🔄 独立事件与互斥事件')
        .fontSize(24).fontWeight(FontWeight.Bold)
        .margin({ bottom: 20 })

      Text('事件概率设置')
        .fontSize(18).fontWeight(FontWeight.Bold)
        .margin({ bottom: 10 })

      Row() {
        Text('P(A): ')
          .width(60)
        Slider({ value: this.pA, min: 0, max: 1, step: 0.01 })
          .width(200)
        Text(this.pA.toFixed(2))
          .width(50)
      }
      .margin({ bottom: 10 })

      Row() {
        Text('P(B): ')
          .width(60)
        Slider({ value: this.pB, min: 0, max: 1, step: 0.01 })
          .width(200)
        Text(this.pB.toFixed(2))
          .width(50)
      }
      .margin({ bottom: 20 })

      Text('实验设置')
        .fontSize(18).fontWeight(FontWeight.Bold)
        .margin({ bottom: 10 })

      Row() {
        Text('实验次数: ')
          .width(80)
        Slider({ value: this.trials, min: 100, max: 10000, step: 100 })
          .width(200)
        Text(this.trials.toString())
          .width(60)
      }
      .margin({ bottom: 20 })

      Row() {
        Button('独立事件模拟')
          .width(120)
          .onClick(() => {
            this.eventType = '独立事件'
            this.simulateIndependent()
          })
        Button('互斥事件模拟')
          .width(120)
          .onClick(() => {
            this.eventType = '互斥事件'
            this.simulateMutuallyExclusive()
          })
      }
      .margin({ bottom: 20 })

      if (this.eventType) {
        Text(`${this.eventType}结果`)
          .fontSize(18).fontWeight(FontWeight.Bold)
          .margin({ bottom: 10 })
      }

      Text(this.result)
        .fontSize(16).fontColor('#2196F3')
        .margin({ bottom: 20 })

      Text('概念解释')
        .fontSize(18).fontWeight(FontWeight.Bold)
        .margin({ bottom: 10 })

      Text('独立事件: 事件A的发生不影响事件B的发生概率，P(AB) = P(A) × P(B)')
        .fontSize(14).fontColor('#666')
        .margin({ bottom: 5 })

      Text('互斥事件: 事件A和事件B不能同时发生，P(A∪B) = P(A) + P(B)')
        .fontSize(14).fontColor('#666')
    }
    .padding(20)
  }

  private simulateIndependent() {
    let countA = 0
    let countB = 0
    let countAB = 0

    for (let i = 0; i < this.trials; i++) {
      const eventA = Math.random() < this.pA
      const eventB = Math.random() < this.pB
      if (eventA) countA++
      if (eventB) countB++
      if (eventA && eventB) countAB++
    }

    const pA = countA / this.trials
    const pB = countB / this.trials
    const pAB = countAB / this.trials
    const pAxB = pA * pB
    const difference = Math.abs(pAB - pAxB)

    this.result = `实验次数: ${this.trials}\n` +
                  `P(A) = ${pA.toFixed(3)}, P(B) = ${pB.toFixed(3)}\n` +
                  `P(AB) = ${pAB.toFixed(3)}, P(A)×P(B) = ${pAxB.toFixed(3)}\n` +
                  `差值: ${difference.toFixed(4)}\n` +
                  `结论: ${difference < 0.05 ? '符合独立事件条件' : '不符合独立事件条件'}`
  }

  private simulateMutuallyExclusive() {
    let countA = 0
    let countB = 0
    let countAB = 0

    for (let i = 0; i < this.trials; i++) {
      const r = Math.random()
      if (r < this.pA) {
        countA++
      } else if (r < this.pA + this.pB && this.pA + this.pB <= 1) {
        countB++
      }
    }

    const pA = countA / this.trials
    const pB = countB / this.trials
    const pAorB = (countA + countB) / this.trials
    const pAplusB = this.pA + this.pB
    const difference = Math.abs(pAorB - pAplusB)

    this.result = `实验次数: ${this.trials}\n` +
                  `P(A) = ${pA.toFixed(3)}, P(B) = ${pB.toFixed(3)}\n` +
                  `P(A∪B) = ${pAorB.toFixed(3)}, P(A)+P(B) = ${pAplusB.toFixed(3)}\n` +
                  `差值: ${difference.toFixed(4)}\n` +
                  `结论: ${difference < 0.05 ? '符合互斥事件条件' : '不符合互斥事件条件'}`
  }
}