To travel from London to Brussels you take the train to Dover, the ferry to Ostend and then the train to Brussels. The train to Dover runs with probability 3/4, the ferry with probability 4/5, and the train to Brussels with probability 2/3. The three events are pairwise independent and at least one of the three transport modes (i.e., the ferry and the two trains) is operational. What is the probability that you arrive in Brussels?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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To travel from London to Brussels you take the train to Dover, the ferry
to Ostend and then the train to Brussels. The train to Dover runs with
probability 3/4, the ferry with probability 4/5, and the train to Brussels
with probability 2/3. The three events are pairwise independent and at
least one of the three transport modes (i.e., the ferry and the two trains)
is operational. What is the probability that you arrive in Brussels?

The answer is said to be 5/12 but i really dont understand why or how, I've been reading through the material and dont get it, Please help

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