Σ學習通 · W20D4 · 121 / 129
0 / 15
第 20 週 · 排列組合與概率 · 第 4 節

集合記法與概率加法定律（互斥、互補）

事件就是「結果的集合」。先用韋恩圖學會並集 A∪B、交集 A∩B、補集 A'，再把它們變成概率加法定律 P(A∪B)=P(A)+P(B)−P(A∩B)；互斥直接相加，互補概率和為 1。配滿圖例。

▶ 第一關： 集合記法（並集、交集、補集）
UABA∩BA∪B = all shaded · outside = complement
ABA∪B = both circles together (A or B)
ABA∩BA∩B = overlap only (A and B)
UAA'A' = everything outside A (U − A)
▶ 第二關： 概率加法定律（減交集）
even2 4> 456P(A∪B) = 3/6 + 2/6 − 1/6 = 4/6 = 2/3
P(A)+P(B)−P(A∩B)=P(A∪B)subtract the overlap counted twice
▶ 第三關： 互斥事件（直接相加）
< 31 2> 45 6nooverlapdisjoint → P = 2/6 + 2/6 = 4/6 = 2/3
disjoint (互斥)P = P(A)+P(B)overlap (重疊)−P(A∩B) neededcheck overlap first, then choose
⚔ BOSS： 互補事件與綜合概率
P(A)P(A')P(A) + P(A') = 1 (whole bar = 1)
heart 13face 12both 3J Q K13/52 + 12/52 − 3/52 = 22/52 = 11/26