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There are two dogs Ralph and Peter. Peter likes barking with the neighbor's dog but Ralph could take it or leave it. However, Ralph is

There are two dogs Ralph and Peter. Peter likes barking with the neighbor's dog but Ralph could take it or leave it. However, Ralph is much more likely to engage in the activity when he hears Peter barking at the fence.

When the neighbor's dog is out, Peter engages in barking 50% of the time, and Ralph engages 10% of the time, and both Ralph and Peter do it 7% of the time.

  1. What is the probability that both dogs engage in barking when the neighbor's dog is out?
  2. What is the probability that neither dogs engage in barking when the neighbor's dog is out?
  3. What is the probability ONLY Ralph engages in barking when the neighbor's dog is out?
  4. Are the events of Ralph and Peter barking when the neighbor's dog is out independent? EXPLAIN briefly.
  5. Are the events of Ralph and Peter barking when the neighbor's dog is out mutually exclusive? EXPLAIN briefly.

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