Foundation and Higher · tree diagrams

Probability trees.
Multiply along,
add down.

and the branches
always sum to 1

two things happen in a row —

And · Or

A and B: multiply along the branches

this route or that route: add

step 1 of 4

Draw the tree

1. 3 red, 2 blue. Pick, replace, pick again.

2. Second pick: the same probabilities.

✓ Each pair of branches adds to 1

step 2 of 4

Multiply along

1. Red and red: follow the top route.

2. Multiply the probabilities along it.

✓ P(R, R) = 35 × 35 = 925

step 3 of 4

Add the routes

1. One of each: R then B, or B then R.

2. Work out each route, then add them.

✓ 625 + 625 = 1225

step 4 of 4

Without replacement

1. Not put back: only 4 counters are left.

2. Took a red? Then only 2 reds are left.

✓ P(R, R) = 35 × 24 = 620 = 310

tree diagrams —

Along a route

multiply

Several routes

add

Not replaced

numerator and denominator drop

“At least one” is quicker as
1 − P(none).

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