Question

Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Suppose that E denotes the event that the first airline's flight is fully booked on a particular day, and F denotes the event that the second airline's flight is fully booked on that same day. Suppose that P(E) = 0.7, P(F) = 0.6, and P(E ∩ F) = 0.49. Calculate P(E | F) the probability that the first airline's flight is fully booked given that the second airline's flight is fully booked.

Answer 1

Answer: 0.8167

Explanation:

Let E denotes the event that the first airline's flight is fully booked on a particular day, and F denotes the event that the second airline's flight is fully booked on that same day.

Given : P(E) = 0.7, P(F) = 0.6, and P(E ∩ F) = 0.49.

Then, by conditional probability formula , we have

`P(E|F)=(P(\cap F))/(P(F))\\\\=(0.49)/(0.6)=0.816666666667\approx0.8167`

Hence, the probability that the first airline's flight is fully booked given that the second airline's flight is fully booked.= 0.8167