3. In air traffic management, air traffic controllers send radio messages to pilots. On receiving a message, the pilot repeats it back to the controller to check that it has been understood correctly. At a particular site, on average \(4 \%\) of messages sent by controllers are not repeated back correctly and so have been misunderstood. You should assume that instances of messages being misunderstood occur randomly and independently.

1. Find the probability that exactly 2 messages are misunderstood in a sequence of 50 messages.
2. Find the probability that in a sequence of messages, the 10th message is the first one which is misunderstood.
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3. Find the probability that in a sequence of 20 messages, there are no misunderstood messages. [1]
4. Determine the expected number of messages required for 3 of them to be misunderstood.
5. Determine the probability that in a sequence of messages, the 3rd misunderstood message is the 60th message in the sequence.
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