Venn Diagrams and Tree Diagrams

Key Questions

  • They can make you see whether you can ADD probabilities or have to multiply.

    Let's take the tree first. You throw three coins. What are the chances there are at least two heads? Draw the tree!
    First split: H 0.5 -- T 0.5 let's do the H to the left.
    Second splits: again H 0.5 -- T 0.5
    So H-H has a chance of 0.5 times 0.5 = 0.25 and we can stop left-left
    T-T is already a looser (0.25)
    We still have H-T and T-H each with a chance of 0.25
    Third throw: they both have a chance of 0.5 so:
    H-T-H = 0.5 x 0.25 = 0.125
    T-H-H = 0.5 x 0.25 = 0.125
    Adding up, we have 0.25 + 0.125 + 0.125 =0.5
    If we had wanted to know the chance of exactly two heads we would have had to go on with the left-left, because H-H-H would then be excluded.
    Summary: down a tree, you multiply -- at the ends you add.