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What is the probability that a random point on AB will be closer to point A than to...

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chihuahuadog12 | Student, Grade 10 | (Level 3) eNoter

Posted April 5, 2013 at 1:57 AM via web

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What is the probability that a random point on AB will be closer to point A than to point X?

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violy | High School Teacher | (Level 3) Assistant Educator

Posted April 5, 2013 at 3:53 AM (Answer #1)

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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.

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