3个概率公式的证明,Prove the following assertions.
问题描述：
3个概率公式的证明,Prove the following assertions.
1.P[A1∩A2∩A3∩.An]>=P[A1]+P[A2]+...+P[An]-(n-1) for any events A1,A2,...An
2.-1/4
答
1.Using mathematical induction,when n=1,equality holds;when n=2,the inequality is just P[A1∪A2]=P[A1]+P[A2]+...+P[A(k-1)]+P[Ak∩A(k+1)]- (k-1)>=P[A1]+P[A2]+...+P[A(k-1)]-(k-1)+P[Ak]+P[A(k+1)]-1=P[A1]...