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(mauve)&=2/3 ⇔ P(mauve)=240^(∘)/360^(∘)
The purple and mauve central angles occupy a total of 90^(∘)+240^(∘)=330^(∘). Since the spinner is 360^(∘), the green region must have a central angle of 30^(∘).
