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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)

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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

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