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It has been determined that 15% of drivers checked at a road stop show traces of...

It has been determined that 15% of drivers checked at a road stop show traces of alcohol and 20% of drivers checked do not wear seat belts. In addition, it has been observed that the two infractions are independent from one another. If an officer stops seven drivers at random:

  1. Calculate the probability that exactly 4 of the drivers have committed any one of the two offenses.
  2. Calculate the probability that at least one of the drivers checked has committed at least one of the two offenses.

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