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The probability that a call to the fire department is unjustified is \(0.19\). We consider a sequence of 3 calls.
  1. What hypothesis must be made to model this situation as a Bernoulli scheme?
  2. Let \(X\) be the random variable that counts the number of unjustified calls. Represent this situation with a tree diagram, indicating the value of \(X\) at the end of each path.
  3. Using the tree, calculate:
    1. the probability that exactly two of the three calls are unjustified: \(P(X=2)\)
    2. the probability that at least one call is justified: \(P(X \ge 1)\)

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