Next, place a protractor along the radius and measure a 60^(∘) angle.
Finally, we will draw a segment between the circle's midpoint and the mark.
Having sketched a picture of the spinner, we should paint the bigger region blue and the smaller region red.
b The probability of landing on blue is the ratio of the blue region's central angle to 360^(∘).
P(blue)=300^(∘)/360^(∘)=5/6
According to the Multiplication Rule of Probability, we have to multiply the probability of landing on blue twice to obtain the probability of P(blue,blue).
c To find the area of the sector, we have to multiply the area of the spinner with the ratio of the sector's central angle to 360^(∘).
A=(7)^2π (300^(∘)/360^(∘)) = 128.28cm^2
d By multiplying the numerator and denominator of both probabilities so that the denominator equals 360^(∘), we can determine the central angle of each region.
P(purple)&=1/4 ⇔ P(purple)=90^(∘)/360^(∘) [1em]
P(yellow)&=2/3 ⇔ P(yellow)=240^(∘)/360^(∘)
The purple and yellow central angles occupy a total of 90^(∘)+240^(∘)=330^(∘) Since the spinner is 360^(∘), the green region must have a central angle of 30^(∘).
