SME
Grade 7 Math · Problem type
Tree diagram
Use this for “A coin is flipped and a spinner with 3 sectors spun. How many outcomes are there, and what is the chance of heads (A) and 2?”
Diagram
n = a × b = 2 × 3 = 6 outcomes
P(A, 2) = 1/2 × 1/3 = 1/6
This is an example. Choose your own values to start a new problem.
n
=
a
×
b
P
Chance of one outcome
worked out (not typed)
Formulas
n
=
a
×
b
(outcomes
in
all
=
first-stage
outcomes
×
second-stage
outcomes)
6 = 2 × 3
P
=
1
÷
n
(chance
of
one
outcome
=
1
÷
outcomes
in
all)
1
6
=
1
÷
6
Assumptions
•
Each stage has equally likely outcomes: a coin has 2 (heads A, tails B), a spinner with 3 sectors has 3.
•
Each branch of the first stage splits into every outcome of the second: multiply.
•
One path, like A then 2, is one of those equally likely outcomes. For three stages, multiply again.
Step-by-step
WE KNOW
a = 2 (first-stage outcomes), b = 3 (second-stage outcomes)
FIND
outcomes in all (n), chance of one outcome (P)
Step 1 · Find outcomes in all (n)
Use n = a × b (outcomes in all = first-stage outcomes × second-stage outcomes)
Each first-stage outcome branches into every second-stage outcome.
n
=
2
×
3
n
=
6
Step 2 · Find chance of one outcome (P)
Use P = 1 ÷ n (chance of one outcome = 1 ÷ outcomes in all)
One path, such as A then 2, is one of the equally likely outcomes.
P
=
1
6
P
=
1
6
Check
Put the numbers back in. Both sides should match.
6 = 2 × 3 ✓
1
6
=
1
÷
6
✓
Topic check
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