SME
Grade 10 Math · Problem type
Listing equally likely outcomes
Use this for “Three coins are tossed. What is the chance of exactly two heads?”
Diagram
n = a × b × c = 2 × 2 × 2 = 8 outcomes
This is an example. Type your own values to start a new problem.
3
8
P
=
f
×
×
n
Outcomes in all
worked out (not typed)
Formulas
n
=
a
×
b
×
c
8 = 2 × 2 × 2
P
=
f
n
3
8
=
3
8
Assumptions
•
A tree lists every outcome: each branch splits into every outcome of the next stage.
•
When every path is equally likely, P(event) = favorable outcomes ÷ all outcomes.
•
A stage of 2 is a coin (H, T), of 3 a spinner (R, G, B), of 4 a four-sided die (1 to 4).
Step-by-step
WE KNOW
a = 2, b = 2, c = 2, f = 3
FIND
outcomes in all (n), probability (P)
Step 1 · Find outcomes in all (n)
Use n = a × b × c
Each branch splits into every outcome of the next stage: multiply.
n
=
2
×
2
×
2
n
=
4
×
2
n
=
8
Step 2 · Find probability (P)
Use P = f ÷ n
Favorable outcomes over all the equally likely outcomes.
P
=
3
8
P
=
3
8
Check
Put the numbers back in. Both sides should match.
8 = 2 × 2 × 2 ✓
3
8
=
3
8
✓
Topic check
See what you know: 5 questions on this topic
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