Weather and Daily Decision Tree Diagrams Exercise

Weather and Daily Decision Tree Diagrams

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Weather and Daily Decision Tree Diagrams

Use tree diagrams to model outcomes and probabilities for daily decisions based on weather conditions.

Questions

  1. MultiChoice

    Weather forecast: Rain (0.4) or No Rain (0.6). Umbrella choice: Yes (0.8 if Rain, 0.1 if No Rain). What is P(Rain AND Take Umbrella)?

  2. MultiChoice

    Using the weather tree diagram, what is P(No Rain AND Take Umbrella)?

  3. MultiChoice

    Using the weather tree diagram, what is the total probability of taking an umbrella P(Take Umbrella)?

  4. MultiChoice

    Bus is On Time (0.7) or Late (0.3). If On Time, catch train (0.9). What is P(On Time AND catch train)?

  5. MultiChoice

    Bus is On Time (0.7) or Late (0.3). If Late, catch train (0.2). What is P(Late AND catch train)?

  6. MultiChoice

    Using the bus/train tree diagram, what is the total probability of catching the train?

  7. MultiChoice

    Student studies (0.8) or does not study (0.2). Passes exam: 0.9 if studies, 0.3 if not. What is P(Studies AND Passes)?

  8. MultiChoice

    Using the study/exam tree diagram, what is P(Does not study AND Passes)?

  9. MultiChoice

    Using the study/exam tree diagram, what is the overall probability that the student passes?

  10. MultiChoice

    In any tree diagram, what must the sum of probabilities on all branches coming out of a single node equal?

  11. MultiChoice

    If P(Studies)=0.8 and P(Fails given studies)=0.1, what is P(Studies AND Fails)?

  12. MultiChoice

    If P(Does not study)=0.2 and P(Fails given not study)=0.7, what is P(Does not study AND Fails)?