SME
Grade 7 Math · Problem type
Two dice
Use this for “Two dice are rolled. What is the chance the sum is 7?”
Diagram
Red die down the side, white die across the top: 36 equally likely pairs.
k = 6 pairs have a sum of 7.
P(sum of 7) = 6/36 = 1/6
This is an example. Type your own values to start a new problem.
s
Sum
example
k
Pairs with that sum
worked out (not typed)
P
Chance of that sum
worked out (not typed)
Formulas
pairs
with
a
sum
of
s
:
k
(the
cells
of
the
grid
with
that
sum:
pairs
with
that
sum)
pairs with a sum of 7: 6
P
=
k
÷
36
(chance
of
that
sum
=
pairs
with
that
sum
÷
36)
1
6
=
6
÷
36
Assumptions
•
Each die is fair: every face is as likely as any other.
•
The 36 pairs of faces are equally likely.
•
Count the cells of the grid with the sum, then divide by 36.
Step-by-step
WE KNOW
s = 7 (sum)
FIND
pairs with that sum (k), chance of that sum (P)
Step 1 · Find pairs with that sum (k)
Use pairs with a sum of s: k (the cells of the grid with that sum: pairs with that sum)
Count the cells of the grid that show the sum.
pairs
with
a
sum
of
7:
k
1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1
k
=
6
Step 2 · Find chance of that sum (P)
Use P = k ÷ 36 (chance of that sum = pairs with that sum ÷ 36)
The pairs with the sum out of all 36 equally likely pairs.
P
=
6
36
P
=
1
6
Check
Put the numbers back in. Both sides should match.
1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1: 6 pairs ✓
1
6
=
6
÷
36
✓
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