SME
Grade 7 Math · Problem type
A bag of marbles
Use this for “A bag has 5 red, 3 blue and 2 green marbles. What is the chance of blue?”
Diagram
n = 5 + 3 + 2 = 10 marbles
P(blue) = 3/10
This is an example. Type your own values to start a new problem.
n
=
r
+
b
+
g
3
10
P
=
b
n
Formulas
n
=
r
+
b
+
g
(marbles
in
all
=
red
marbles
+
blue
marbles
+
green
marbles)
10 = 5 + 3 + 2
P
=
b
÷
n
(chance
of
blue
=
blue
marbles
÷
marbles
in
all)
3
10
=
3
÷
10
Assumptions
•
The marbles are the same size and feel the same.
•
Each marble is as likely to be drawn as any other.
•
The chance of blue is the blue marbles out of all the marbles.
Step-by-step
WE KNOW
r = 5 (red marbles), b = 3 (blue marbles), g = 2 (green marbles)
FIND
marbles in all (n), chance of blue (P)
Step 1 · Find marbles in all (n)
Use n = r + b + g (marbles in all = red marbles + blue marbles + green marbles)
Add the marbles of every color.
n
=
5
+
3
+
2
n
=
8
+
2
n
=
10
Step 2 · Find chance of blue (P)
Use P = b ÷ n (chance of blue = blue marbles ÷ marbles in all)
The blue marbles out of all the marbles.
P
=
3
10
P
=
3
10
Check
Put the numbers back in. Both sides should match.
10 = 5 + 3 + 2 ✓
3
10
=
3
÷
10
✓
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