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

Step-by-step 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

$P(E|F)=\dfrac{P(\cap F)}{P(F)}\\\\=\dfrac{0.49}{0.6}=0.816666666667\approx0.8167$

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