SME
Grade 7 Math · Problem type
Tree diagram with three stages
Use this for “A coin is flipped three times (A = heads, B = tails). What is the chance of heads all three times?”
Diagram
n = a × b × c = 2 × 2 × 2 = 8 outcomes
P(A, A, A) = 1/2 × 1/2 × 1/2 = 1/8
This is an example. Choose your own values to start a new problem.
n
=
a
×
b
×
c
P
Chance of one outcome
worked out (not typed)
Formulas
n
=
a
×
b
×
c
(outcomes
in
all
=
first-stage
outcomes
×
second-stage
outcomes
×
third-stage
outcomes)
8 = 2 × 2 × 2
P
=
1
÷
n
(chance
of
one
outcome
=
1
÷
outcomes
in
all)
1
8
=
1
÷
8
Assumptions
•
Each stage has equally likely outcomes, named A, B, …: a coin has 2 (heads A, tails B), a spinner with 3 sectors has 3.
•
Every path through the three stages is one outcome: multiply the three counts.
•
The chance of one path is 1 out of all of them: the three branch chances multiplied.
Step-by-step
WE KNOW
a = 2 (first-stage outcomes), b = 2 (second-stage outcomes), c = 2 (third-stage outcomes)
FIND
outcomes in all (n), chance of one outcome (P)
Step 1 · Find outcomes in all (n)
Use n = a × b × c (outcomes in all = first-stage outcomes × second-stage outcomes × third-stage outcomes)
Each branch splits into every outcome of the next stage, twice over.
n
=
2
×
2
×
2
n
=
4
×
2
n
=
8
Step 2 · Find chance of one outcome (P)
Use P = 1 ÷ n (chance of one outcome = 1 ÷ outcomes in all)
One path, such as heads three times (A, A, A), is one of the equally likely outcomes.
P
=
1
8
P
=
1
8
Check
Put the numbers back in. Both sides should match.
8 = 2 × 2 × 2 ✓
1
8
=
1
÷
8
✓
Topic check
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