probability

Probability Level 4

If three points P,Q and R are taken at random on the circumference of the circle, then find the probability that they do not lie on the same semi-circle.


The answer is 0.25.

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Fox To-ong
Feb 9, 2015

thats 1/4 of the whole part

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Mayank Khetan
Oct 9, 2014

The no. of ways of selecting a point from a line is clearly directly proportional to its length.

Let total no. of ways of selecting three points from the circumference be x. Therefore, the total no. of ways of selecting three points from one half of the circle will be x/8.(as no. of ways of selecting each point is halved.) Similarly, the no. of ways of selecting 3 points from the other half of the circle will also be x/8.

Thus, reqd. probability=( (x/8)+(x/8) )/ (x/4)=0.25

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