In the accompanying diagram a fair spinner is placed at the center O of the circle. Diameter AOB and radius OC divide the circle into three regions labelled X, Y and Z. If ∠BOC = 45°. What is the probability that the spinner will land in the region X? ( See fig)
Given ∠BOC = 45°
∠AOC = 180° – 45° = 135°
Area of circle = πr2
Area of region X = θ/360°x πr2
= 135/360 x πr2 = 3/8 x πr2
Probability that the spinner will land in the region
X = (Area of region of x)/(total area of circle) = (3/8 x πr2)/πr2 = 3/8
