Let $X,Y$ be two firms. An MBA applies for the job in $X$ and $Y$. The probability he being selected in firm $X$ is $0.7$ and being rejected at $Y$ is $0.5$. Probability of at least one of his applications being rejected is $0.6$. What is the probability that he will be selected in one of the firms?
i.e.,
$P(X)=0.7$, $P(\bar{Y})=0.5$, $1-P(X\cap Y)=0.6$
So, my doubt is,
$P$(he will be selected in one of the firms)
=$P(X\cap \bar{Y})+P(\bar{X}\cap Y)$
or
=$P(X\cup Y)$ {but this means atleast one firm, am i correct}
So, what does the question actually mean.