SME
Grade 7 Math · Statistics & Probability
Probability of simple and compound events
Use this for “A spinner has 3 red, 4 blue and 1 yellow sector. What is the chance of red?”
Diagram
P(red) = 3/8
This is an example. Type your own values to start a new problem.
n
=
r
+
b
+
y
3
8
P
=
r
n
R
Chance of red or blue
worked out (not typed)
Formulas
n
=
r
+
b
+
y
(sectors
in
all
=
red
sectors
+
blue
sectors
+
yellow
sectors)
8 = 3 + 4 + 1
P
=
r
÷
n
(chance
of
red
=
red
sectors
÷
sectors
in
all)
3
8
=
3
÷
8
R
=
(
r
+
b
)
÷
n
(chance
of
red
or
blue
=
(red
sectors
+
blue
sectors)
÷
sectors
in
all)
7
8
=
(3
+
4)
÷
8
Assumptions
•
The spinner is cut into equal sectors.
•
The arrow is as likely to stop in any sector as any other.
•
A probability is a number from 0 (impossible) to 1 (certain): favorable sectors ÷ all sectors.
•
Spin many times: the share of red comes close to the probability.
Step-by-step
WE KNOW
r = 3 (red sectors), b = 4 (blue sectors), y = 1 (yellow sectors)
FIND
sectors in all (n), chance of red (P), chance of red or blue (R)
Step 1 · Find sectors in all (n)
Use n = r + b + y (sectors in all = red sectors + blue sectors + yellow sectors)
Add the sectors of every color.
n
=
3
+
4
+
1
n
=
7
+
1
n
=
8
Step 2 · Find chance of red (P)
Use P = r ÷ n (chance of red = red sectors ÷ sectors in all)
The red sectors out of all the equal sectors.
P
=
3
8
P
=
3
8
Step 3 · Find chance of red or blue (R)
Use R = (r + b) ÷ n (chance of red or blue = (red sectors + blue sectors) ÷ sectors in all)
Red or blue: count both colors’ sectors, then divide by all of them.
R
=
3 + 4
8
R
=
7
8
R
=
7
8
Check
Put the numbers back in. Both sides should match.
8 = 3 + 4 + 1 ✓
3
8
=
3
÷
8
✓
7
8
=
(3
+
4)
÷
8
✓
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