Law of total probability

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Intros
Lessons
  1. Illustrating the Law of Total Probability for two conditional events
  2. The Law of Total Probability for more than two events
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Examples
Lessons
  1. 2 disjoint mutually exclusive events
    Back Country skiers can be divided into two classes, those with avalanche training and those who have no avalanche training. An individual with avalanche training has a probability of 0.05 of getting in an avalanche, while an individual without avalanche training has a probability of 0.20 of being in an avalanche. If 75% of backcountry skiers have avalanche training and 25% of back country skiers do not, then what is the probability that a randomly selected backcountry skier will be in an avalanche?
    1. 3 or more disjoint mutually exclusive events
      I have 3 bags that each contains 5 marbles.

      Bag 1:

      Bag 2:

      Bag 3:

      2 Green

      4 Green

      5 Green

      3 Red

      1 Red

      0 Red



      I choose one bag at random and draw a marble. What is the probability that I draw a green marble?
      1. Thomas is frequently late to work. If it is sunny he will be late with probability 0.15; if it rains he is late with probability 0.05. And if it snows he is late with probability 0.5 (if he shows up at all). The meteorologist has predicted there is a 50% it will be sunny tomorrow, a 35% chance it will rain and a 15% chance it will snow. What is the probability that Thomas will be late tomorrow?

        Make jokes about taking sick days + make pictures for the sun, rain and snow.