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?

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.8: Probabilities Of Disjoint And Overlapping Events
Problem 2C
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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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