**Exercise 6.30: Probability Analysis of Flight Bookings**Two different airlines offer a flight from Los Angeles to New York that departs each weekday morning at the same scheduled time. Define event \( E \) as the occurrence of the first airline's flight being fully booked on a specific day, and event \( F \) as the occurrence of the second airline's flight being fully booked on the same day.Given the probabilities:- \( P(E) = 0.7 \)- \( P(F) = 0.6 \)- \( P(E \cap F) = 0.54 \)**Tasks:**a. Calculate \( P(E|F) \), the conditional probability that the first airline's flight is fully booked given that the second airline's flight is fully booked. (Hint: Refer to Example 6.12 for guidance.)b. Calculate \( P(F|E) \), the conditional probability that the second airline’s flight is fully booked given that the first airline’s flight is fully booked. Consider using the formula for conditional probability:\[ P(E|F) = \frac{P(E \cap F)}{P(F)} \]\[ P(F|E) = \frac{P(E \cap F)}{P(E)} \]

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6.30. Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline's flight is fully booked on a particular day, and let F denote the event that the second airline's flight is fully booked on that same day. Suppose that P(E) = .7, P(F) = .6, and P(EN F) = .54. a. 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. (Hint: See Example 6.12.) b. Calculate P(E|F).

6.30. Two different airlines have a flight from Los Angeles to New York that departs each weekday morning at a certain time. Let E denote the event that the first airline's flight is fully booked on a particular day, and let F denote the event that the second airline's flight is fully booked on that same day. Suppose that P(E) = .7, P(F) = .6, and P(EN F) = .54. a. 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. (Hint: See Example 6.12.) b. Calculate P(E|F).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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