SME
Grade 7 Math · Problem type
Two dice: a sum of at least
Use this for “Two dice are rolled. What is the chance the sum is at least 10?”
Diagram
Red die down the side, white die across the top: 36 equally likely pairs.
k = 6 pairs have a sum of at least 10.
P(sum ≥ 10) = 6/36 = 1/6
This is an example. Type your own values to start a new problem.
s
Smallest sum
example
k
Pairs with that sum or more
worked out (not typed)
P
Chance of that sum or more
worked out (not typed)
Formulas
pairs
with
a
sum
of
at
least
s
:
k
(the
cells
of
the
grid
with
that
sum
or
more:
pairs
with
that
sum
or
more)
pairs with a sum of at least 10: 6
P
=
k
÷
36
(chance
of
that
sum
or
more
=
pairs
with
that
sum
or
more
÷
36)
1
6
=
6
÷
36
Assumptions
•
The 36 pairs of faces are equally likely.
•
“At least 10” means 10, 11 or 12. Count the pairs for each sum and add.
•
The chance of “less than 10” is 1 minus the chance of “at least 10”.
Step-by-step
WE KNOW
s = 10 (smallest sum)
FIND
pairs with that sum or more (k), chance of that sum or more (P)
Step 1 · Find pairs with that sum or more (k)
Use pairs with a sum of at least s: k (the cells of the grid with that sum or more: pairs with that sum or more)
Count the pairs for each sum from the smallest up to 12, then add.
pairs
with
a
sum
of
at
least
10:
k
sum 10: 3, sum 11: 2, sum 12: 1
k
=
6
Step 2 · Find chance of that sum or more (P)
Use P = k ÷ 36 (chance of that sum or more = pairs with that sum or more ÷ 36)
Those pairs out of all 36 equally likely pairs.
P
=
6
36
P
=
1
6
Check
Put the numbers back in. Both sides should match.
3 + 2 + 1 = 6 ✓
1
6
=
6
÷
36
✓
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