Points and Plane!

Probability Level 3

2 points are drawn in a plane such that the distance between them is less than 2.The probability that the distance between them is at least 1 can be expressed as $\dfrac{m}{n}$ , where $m$ and $n$ are coprime positive integers. Find $m+n$ .

The answer is 7.

1 solution

Shivam Mishra
Apr 24, 2016

Fix one point. Now, the locus of the possible points for our second point is within a circle of radius $2$ . Draw out the circle. The locus of points that are distance $1$ from this point is a circle of radius $1$ . Our probability is just the difference of areas: $\frac{3}{4}$ , so $m+n=7$

Moderator note:

Good usage of the geometric probability.

The problem could be phrased clearer about the probability distribution of these points.

Points and Plane!

The answer is 7.

1 solution

Moderator note:

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