题目
已知 p(A)=0.4,p(B)=0.3,p(A cup B)=0.5,则 p(A-B)= [填空1] ;p(B-A)= [填空2] 。A-B = A cup B - Bp(A-B) = p((A cup B)-B)= p(A cup B) - p(B) = 0.2
已知 $p(A)=0.4$,$p(B)=0.3$,$p(A \cup B)=0.5$,则 $p(A-B)=$ [填空1] ;$p(B-A)=$ [填空2] 。
$A-B = A \cup B - B$
$p(A-B) = p((A \cup B)-B)$
$= p(A \cup B) - p(B) = 0.2$
题目解答
答案
已知 $P(A) = 0.4$,$P(B) = 0.3$,$P(A \cup B) = 0.5$,利用并集公式求交集概率:
$P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.4 + 0.3 - 0.5 = 0.2$
计算 $P(A - B)$ 和 $P(B - A)$:
$P(A - B) = P(A) - P(A \cap B) = 0.4 - 0.2 = 0.2$
$P(B - A) = P(B) - P(A \cap B) = 0.3 - 0.2 = 0.1$
或者,利用 $A - B = (A \cup B) - B$ 和 $B - A = (A \cup B) - A$:
$P(A - B) = P(A \cup B) - P(B) = 0.5 - 0.3 = 0.2$
$P(B - A) = P(A \cup B) - P(A) = 0.5 - 0.4 = 0.1$
答案:
$P(A - B) = \boxed{0.2}$,$P(B - A) = \boxed{0.1}$