I'm scratching my head over this probability problem - can you help me figure out where I'm going wrong?
The problem states:
$P(A) = P(B) = P(C) = 0.25;$
$P(\color{red}{B}C) = 0;$
$P(AB) = P(AC) = 0.15.$
The question asks: What is the probability that at least one of A, B, or C occurs?
The provided solution is $0.45,$ using the formula:
$P(A ~\text{or} ~B ~\text{or} ~ C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(AC) + P(A ~\color{red}{\text{and}} ~B ~\color{red}{\text{and}} ~C).$
But here's what's confusing me -
if $~P(AC)=0 ~\text{and} ~P(AB)=P(AC)=0.15,~$
shouldn't $~P(AB) + P(AC)~$ already be $~0.3~$?
That is, the probability value of $~P(AC)~$ cannot be 0.