a What is the probability of getting any of the three regions?
B
b Each sector's area must reflect the same ratio of the whole spinners area as the probability of spinning that sector.
C
c Do you necessarily have to have only one sector that is blue, one that is white and one that is red?
A
a P(blue)=50 %
B
bSketch:
C
cExample Solution:
Practice makes perfect
a From the exercise, we know that the spinner only has three regions, red, white, and blue. Since the probability of getting one of these regions is 100 %, we can find the probability of getting P(blue) by subtracting P(red) and P(white) from 100 %.
b From Part A, we know the probability of spinning each of the three regions.
P(blue)&=0.5
P(red)&=0.4
P(white)&=0.1
For these probabilities to be true, each sector's area must reflect the same ratio of the whole spinners area. The area depends on how large the sector's angle is, and since a circle is 360^(∘), we can write three equations describing the three angles. We will label these angles x, y and z.
P(blue): x/360^(∘)=0.5 &⇔ x = 180^(∘) [0.8em]
P(red): y/360^(∘)=0.4 &⇔ y = 144^(∘) [0.8em]
P(white): z/360^(∘)=0.1 &⇔ z = 36^(∘)
To create this spinner, we will use a protractor. By drawing the circle's diameter, we can illustrate the blue region.
Next, we will measure an angle of 144^(∘) to create the red region. Whatever is left will be the white region.
Let's remove the protractor and add the measures of our three central angles.
c As long as the sum of the blue, red and white regions central angle add up to 180^(∘), 144^(∘) and 36^(∘), the spinner can have any number of regions. Below we see an example.
This is a different spinner but it's blue, red, and white regions still cover the same amount of area. Therefore, the probability of getting the three regions is unchanged.
