Could someone please check my work?

If A and B are independent, show that so are ( a) A and BC WTS- P(ABC ) = PCASPCBC) ( 6 ) Ac and B C - WTS PCACBC ) = PLAC ) PCB= ) Since A and B are independent , PCAB ) = PCA )PCB ) Regardless of independence, PCA=) = 1-PCA ) P(B= ) = 1 - PCB) and PCAUB) = PCA) + PCB) PLAUB ( a ) ( P CA ) P ( B C ) = PCA ) [ 1 - PCB )] = PCA) PCA)PCB) = PCA) - PCAB) ABC AB = P(ABC ) P(A) - PCAB) = P(ABC) S=1 ( b ) . P ( A c ) P ( B = ) = [1- PCA)] [1-PCB)] = 12-PCB)-PCA)+ PLA)PCB) A B = 1 - PCB)-PCA) + P(AB) A NBC = 1-[PCB) + PCA)-PCAB) = 1- P(AUB) = PCAUB) AUB P (AUB)