三章概率.pptVIP

Try other examples using this table. Let students solve first. Allow about 20 minutes for this. Try other examples using this table. Let students solve first. Allow about 10 minutes for this. 总结 定义实验，结果，样本点，样本空间，事件和概率 使用温氏图、二维表和树图来找到概率 描述和使用概率规则 As a result of this class, you will be able to ... Other compound events could be formed: Tail on the second toss {HT, TT} At least 1 Head {HH, HT, TH} Typically, the last event (Heads on Both) is called a simple event. Let students solve first. Allow about 20 minutes for this. Mutually Exclusive What is the intersection of mutually exclusive events? The null set. Try other examples using this table. Let students solve first. Allow about 10 minutes for this. 互补事件 事件A的补集 A不发生的事件 所有不属于A的事件: AC P(A) + P(AC) = 1 S AC A S 黑色 事件补集例子 事件 黑色: 2B?, 2B?, ..., AB? 事件黑色的补集, BlackC: 2R?, 2R?, ..., AR?, AR? 样本空间: 2R?, 2R?, 2B?, ..., AB? 实验: 抽1张牌. 观测种类，颜色和花色 附加规则 互斥事件 复合事件 CompoundEvents A or B A and B Not A A given B 互斥事件 不同时发生的事件 A ? B 不包含的任何样本 ? ? 互斥事件 S ? ? 互斥事件例子 事件 ? 和? 是互斥的 实验: 抽1张牌. 观测种类，颜色和花色 事件 红桃: 2?, 3?, 4? , ..., A? 样本空间: 2?, 2?, 2?, ..., A? 事件黑桃: 2?, 3?, 4?, ..., A? 附加规则 用于计算事件并集的复合概率 P(A OR B) = P(A ? B)  = P(A) + P(B) – P(A ? B) 对于互斥事件而言: P(A OR B) = P(A ? B) = P(A) + P(B) 附加规则例子 实验: 抽1张牌. 观测种类，颜色和花色 P(Ace ? Black) = P(Ace) + P(Black) – P(Ace Black) ? Color Type Red Black Total Ace 2 2 4 Non-Ace 24 24 48 Total 26 26 52 52 52 52 52 4 26 2 28 = + – = 思考 P(A ? D) = P(B ? C) = Event Event C D Total A 4 2 6 B 1 3 4 Total 5 5 10 使用附加规则, 什么是概率? 10 10 10 10 6 5 2 9 结果* 使用附加规则结果是: P(A ? D) = P(A) + P(D) – P(A ? D) 1. 2. P(B ? C) = P(B) + P(C) – P(B ? C) 10 10 10 10 4 5 1 8 = + – = = + – = 条件概率 复合事件 CompoundEvents A or B A and B Not A A given B 条件概率 1. 假定另一事件已经发生该事件的概率 2. 修正原样本空间以计算新的信息 排除某些结果 3. P(A | B) = P(A and B)