Exercise [22.28]

deant · 02 Jan 2013, 14:16

Referring to Fig. 22.11, but allowing for possibly different size diameters, we have:

$Radius = \overline{OA} = \overline{OA^\prime} = \overline{OB}$

so

$\overline{A^\prime C}\div\overline{A^\prime A} \;\; = \;\; \frac{\overline{OA^\prime} + \overline{OB}\cos\theta}{2\overline{OA}} \;\; = \;\; \frac{1}{2}\left(1+\cos\theta\right)$

...and we established previously that this expression gives the probability of a YES result.

$\blacksquare$