What is the probability that a random point on AB will be closer to point A than to point X? http://www.flickr.com/photos/93084714@N07/8621084580/in/photostream

Expert Answers
violy eNotes educator| Certified Educator

The points to the right of point X are closer to X. 

So, we are left on finding how many points our closer to point A from 0 to 8. Dividing the segment AX, the middle point will fall at 4. 

Point A and point X are equally close to the middle point. But, the points to the left of the middle point including the point A itself is closer to point A. Counting the points on the left of middle point (point at 4), 0, 1, 2, 3. Therefore there are 4 points closer to point A. 

Use the formula: 

P(event) = (size of successful region)/(size of total region).

We will have: 

Probability that a random point on AB will closer to point A than point X is: 4/12 = 1/3.