Lesson

In general, the probability of an event occuring is: P\left(\text{Event}\right)=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

This can be applied to geometric contexts in one, two, or three dimensions.

For lengths: P\left(\text{Event}\right)=\dfrac{\text{Length of favorable segment}}{\text{Total length}}

For areas: P\left(\text{Event}\right)=\dfrac{\text{Area of favorable region}}{\text{Total area}}

For volumes: P\left(\text{Event}\right)=\dfrac{\text{Volume of favorable space}}{\text{Total volume}}

A random point is chosen along \overline{AD}.

a

Find the probability that the point is on \overline{AB}

b

Find the probability that the point is on \overline{AC}

The probability of a random point on this image being inside the circle is 0.252. If the rectangle is 24\, \text{ft} \times 13\, \text{ft} , determine the radius of the circle.