YTC 發問於 科學及數學數學 · 6 年前

F.5 Maths probability

Picture: http://postimg.org/image/59sjelm7v/

In this question, I try to use a Venn diagram to find the formula in the blue

rectangle. However, i found that I also need to use this formula in another

questions, but I cannot find this formula in the textbook.

I want to ask is this formula is already proved? Is there any other formula about

probability that is very useful but do not mention in textbook?

Thank you!

更新:

RE 知足常樂:

請問 'set rule' 有沒有中文名稱?

我嘗試在網上搜尋set rule但是完全找不到相關資料......

1 個解答

評分
  • 6 年前
    最愛解答

    Probability Rule:

    If events A and B are mutually exclusive, then

    P(A or B) = P(A) + P(B).

    Set Rule:

    For any sets (events) A and C, A can be partitioned into two parts, one is with C, one is without C. That is,

    A = ( (A and C) or (A and C') )

    Clearly (A and C) and (A and C') are two mutually exclusive events.

    There is no overlapping part in the Venn diagram.

    Therefore,

    P(A)

    = P( (A and C) or (A and C') )

    = P(A and C) + P(A and C')

    Other formulae:

    P(A or B) = P(A) + P(B) - P(A and B) [must be true]P(A or B) = P(A) + P(B) [if A and B are mutually exclusive, i.e., P(A and B) = 0]P(A and B) = P(A | B)P(B) = P(B | A)P(A) [must be true]P(A and B) = P(A)P(B) [if A and B are independent]Actually the set rule mentioned above is not strange to you, you also encounter this in the tree diagram.Suppose your tree is:    / B

       /

     A -- B’

     A’ -- B

       \

        \ B’

    Then, you also know that

    P(B) = P(A)P(B|A) + P(A')P(B|A')

    That is actually just

    P(B) = P(B and A) + P(B and A')

    2015-03-29 15:13:23 補充:

    我以上打的 Set Rule 不是專有名詞,只是一句普通的英文,指 some rules about the concept of "set theory".

    如果你對 set theory 有興趣可以看看:

    https://mathtrielhighschool.files.wordpress.com/20...

    由 P.31 起有很多 rules,不是太難明。

    其實把 A 寫成 (A and B) or (A and B') 只是很直接的 partition on B,不是太複雜。

    2015-03-29 15:13:43 補充:

    如果你真的要一個明確的 rule,這個叫 law of total probabilty:

    http://en.wikipedia.org/wiki/Law_of_total_probabil...

還有問題嗎?立即提問即可得到解答。