You travel from Amsterdam to Sidney with change of airplanes in Dubai and Singap

You travel from Amsterdam to Sidney with change of airplanes in Dubai and Singapore. You have one piece of luggage. At each stop your luggage is transferred from one airplane to another. At the airport in Amsterdam there is a probability of 5% that your luggage is not placed in the right plane. This probability is 3% at the airport in Dubai and 2% at the airport in Singapore. What is the probability that your luggage does not reach Sidney with you? If your luggage does not reach Sidney with you, what is the probability that it was lost at the airport of Dubai?

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