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Birds Arrive at a Bird Feeder

Birds arrive at a bird feeder according to a Poisson arrival process with a rate of 6 birds per hour. A person starts watching the feeder at time 0.

  1. What is the probability that the first three birds arrive at the feeder within 30 minutes?
  2. What is the expected time it takes for the 10th bird to arrive?
  3. 10% of the birds who visit the feeder are cardinals. What is the probability that the 3rd cardinal to arrive at the feeder is the 10th bird to arrive at the feeder?
  4. 10% of the birds who visit the feeder are cardinals. The person watching the feeder decides to continue watching the feeder until they see a cardinal. What is the probability that the person waits more than 5 hours?

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