Tree diagrams (basic)

On a tree diagram,

the​ (a)   are written at the ends of the branches,

the ​ (b)   are written above / below the branches.

• outcomes
• probabilities

For any set of branches on a tree diagram, the probabilities must add up to what number?

The diagram shows an incomplete set of branches of a tree diagram.

What is the missing number?

Mathematical Equivalence

ON

The diagram shows an incomplete set of branches of a tree diagram.

What is the missing number?

Mathematical Equivalence

OFF

Mathematical Equivalence

ON

Answer explanation

We multiply the numbers on the branches, so here we do 0.4 x 0.4 = 0.16

Mathematical Equivalence

ON

Answer explanation

We multiply the numbers on the branches, so here we do 0.6 x 0.6 = 0.36

Mathematical Equivalence

ON

Answer explanation

Landing on Heads once can happen in 2 ways, Heads then Tails, or Tails then Heads.

Head then Tails = 0.4 x 0.6 = 0.24

Tails then Heads = 0.6 x 0.4 = 0.24

Total probability = 0.24 + 0.24 = 0.48

Mathematical Equivalence

OFF

Answer explanation

On each set of branches, the probability of getting a six is 2/7

We multiply the numbers on the branches, so here we do 2/7 x 2/7 = 4/49

Mathematical Equivalence

OFF

Answer explanation

Landing on a six at least once means we could get one six or two sixes.

We can get one six in 2 different ways:

Six, not six = 2/7 x 5/7 = 10/49

Not six, six = 5/7 x 2/7 = 10/49

We can get two sixes in only one way:

Six, six = 2/7 x 2/7 = 4/49

Total probability = 10/49 + 10/49 + 4/49 = 24/49

Note: we can calculate this more quickly by thinking about the opposite event - if we do NOT get at least one six that means we get no sixes. Not six, not six = 5/7 x 5/7 = 25/49

So our event has probability 1 - 25/49 = 24/49