Answer:
[tex]P = \frac{2}{3}[/tex]
Step-by-step explanation:
All the points in the plane that are 20 inches from P constituing a circle with center in P and with radius 20 inch
We need find the angle in this circle by which the point R is closer to P than it is to Q. The limit situation occurs when the distances from P to R and from R to Q are equals and have the value 20 inches. In this situation the points P, R y Q form a equilater triangle with angles of value 60°.
Thus, the point R is closer to P than it is to Q in 240° of the circle, except 60° above of the line PQ and 60° below the line PQ.
Then the probability is
[tex]P= \frac{240}{360} = \frac{2}{3}[/tex]
