An airline has 3 flights from Chicago to New York, Atlanta, and Los Angeles. Let $\displaystyle A $ denote the event that the New York flight is full and define events $\displaystyle B $ and $\displaystyle C $ analogously.

And $\displaystyle P(A) = 0.6, \ P(B) = 0.5, \ P(C) = 0.4 $ and the three events are independent. Compute the following probabilities:

(a) all 3 flights are full. at least one flight is not full.

So $\displaystyle P(ABC) = P(A)P(B)P(C) = 0.12 $ and $\displaystyle 1-P(ABC) = 0.88 $.

(b) only the New York flight is full. exactly one of the three flights is full.

So $\displaystyle P(\text{only NY flight is full}) = P(A) - P(AB) - P(AC) + P(ABC) $?

And the probability that exactly one flight is full is: $\displaystyle P(A) - P(AB) - P(AC) + P(ABC) $ $\displaystyle + P(B) - P(AB) - P(BC) + P(ABC) + P(C) - P(AC) - P(BC) + P(ABC) $

are these correct?