Probability of "sold out" A plane has seats in economy class and business class. The probability of "sold out" in at least one of the two classes is $\frac{1}{3}$, while the probability of "sold out" in business class is $\frac{1}{8}$. What is the probability that economy class is "sold out" but business class is not?

Assuming sold out for econ is independent of sold out for business (and its complement), then denoting sold out for econ is E and sold out for bus as B, we can express the facts as following:

$P(E\bigcup B)$=$P(E)+P(B)-P(E\bigcap B)=P(E)+P(B)-P(E)P(B)=P(E)(1-P(B))+P(B)=1/3$ $P(B)=1/8$ implies (via substitution in the above) that $P(E)(1-P(B))=5/24$

The question can be framed as asking what is $P(E\bigcap B^c)$ which is equal to $P(E)P(B^c)=P(E)(1-P(B))$, which was already solved above.