OpenRevise

Flashcards · Maths · Probability

Tree Diagrams

16 cards

  1. What does a tree diagram show?

    All the possible outcomes of events happening one after another, with their probabilities.

  2. What do you do along a path in a tree diagram?

    Multiply the probabilities.

  3. What do you do when more than one path gives the result you want?

    Add the path probabilities.

  4. What should the branches leaving one point add up to?

    1.

  5. What does independent mean for two events?

    The first event does not change the probability of the second.

  6. What is different about the branches for events without replacement?

    The second probabilities depend on the first pick.

  7. What is \(P(\text{at least one})\) in terms of \(P(\text{none})\)?

    \(1 - P(\text{none})\).

  8. Rain has probability 0.3 on each of two days. What is the probability of rain on both days?

    \(0.3 \times 0.3 = 0.09\).

  9. With 3 red and 2 blue counters, what is \(P(\text{two reds})\) without replacement?

    \(\dfrac{3}{5} \times \dfrac{2}{4} = \dfrac{3}{10}\).

  10. With 3 red and 2 blue counters, what is \(P(\text{different colours})\) without replacement?

    \(\dfrac{3}{5}\).

  11. What is the probability of any particular outcome of three coin tosses?

    \(\dfrac{1}{8}\).

  12. How do you check a completed tree diagram?

    The outcome probabilities should add up to 1.

  13. If one branch has probability 0.6, what is the other branch from the same point?

    0.4.

  14. Why does the denominator drop to 4 on the second pick from 5 counters?

    One counter has been taken and not replaced.

  15. What does "with replacement" mean?

    The item is put back, so the probabilities stay the same.

  16. Why is "at least one" often quicker with the opposite?

    Only one path (none) needs calculating instead of several.