WebSep 29, 2024 · 在概率论中,先有事件相等,才有概率相等。. 由概率的单调性,只有条件“B包含于A”成立的时候,才有P (A-B)=P (A)-P (B)成立。. 对于任意两个事件A、B来说,B不一定包含于A,而AB一定包含于A,所以A-B=A-AB,. 所以:P (A-B)=P (A)-P (AB) 2、P (A+B)=P (A)+P (B) :. AB互斥的 ... WebSep 20, 2024 · If independent, P (A and B) = P (A) * P (B) Why is it that we often use P (A)*P (B) for P (A and B), even when the events aren't independent (e.g. no replacement)? For instance, in the conditional probability formula, I've found this dilemma occur often when I'm figuring out P (A and B).
求 在概率论中p(a+b)与p(ab)的意义区别和计算公式_作业帮
WebJan 27, 2024 · Any probability result that is true for unconditional probability remains true if everything is conditioned on some event. You know that by definition, (1) P ( A ∣ B) = P ( A ∩ B) P ( B) and so if we condition everything on C having occurred, we get that. (2) P ( A ∣ ( B ∩ C)) = P ( ( A ∩ B) ∣ C) P ( B ∣ C) WebMar 29, 2024 · Example 31 For any sets A and B, show that P (A ∩ B) = P (A) ∩ P (B). To prove two sets equal, we need to prove that they are subset of each other i.e.. we have to prove P (A ∩ B) ⊂ P (A) ∩ P (B) & P (A) ∩ P (B) ⊂ P ( A ∩ B) Let a set X belong to Power set P (A ∩ B) i.e. X ∈ P ( A ∩ B ). As set X is in the power set of A ... breakpoint icon
若P(AB)=P(A)P(B)那么A、B独立么? - 知乎
WebAug 11, 2009 · 若A与B相互独立. P (AB)=P (A)P (B) 当P (A)>0 P (AB)=P (A)P (B A) 当P (B)>0 P (AB)=P (B)P (A B) 有时候概率为0,比如不相容事件,如A B为2个不相容事件,A 发生了,P (B)=0。. 比如投掷一枚硬币,是正面的情况下,反面概率为0。. 110. 评论. 分享. Web2 Answers. P ( A) = P ( A Ω) = P ( A ∩ ( B ∪ B ′)) = P ( ( A ∩ B) ∪ ( A ∩ B ′)) = P ( A B) + P ( A B ′). Where the last equality stands because AB and AB' have no intersections. Your intuition is correct. If you write it is conditional probability, this should be apparent. breakpoint idea