PROBLEM 14E

Let the interval [−r, r] be the base of a semicircle. If a point is selected at random from this interval, assign a probability to the event that the length of the perpendicular segment from the point to the semicircle is less than r/2.

Answer:

Step1 of 1:

Let the interval [−r, r] be the base of a semicircle.

If a point is selected at random from this interval, assign a probability to the event that the length of the perpendicular segment from the point to the semicircle is less than r/2.

Here, AB = r sin

For AB < r/2 .

r sin <

sin<

Then, < , similarly on the other side of the y-axis .

Therefore , for AB <

To...