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.
Best Answer
Your first suggestion is the formula for "accepted at exactly one firm" (but not at both), the second for "accepted in at least one firm" (and even possibly at both). I vote for the latter.