If a dot is put in the incircle of an equilateral triangle without looking into it,
(a) Find the probability of the dot being inside the incircle
​(b) Find the probability of the dot being outside the incircle.

Dear Student,
Please find below the solution to the asked query:

We know that if r is radius of incircle and s is semiperimeter and  is areaof triangle , thenr=s=34a23a2r=a23Hence area of incircle=πr2=πa23=πa212Hencei Probability of the dot being inside the incircle=Area of incircle=πa21234a2=π33ii Probability of the dot being outside the incircle=1- Probability of the dot being inside the incircle=1-π33

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • 2
In equilateral triangle r = a/2root 3

a is side of triangle

Area of incircle = pi*a^2/12
Area of triangle = root3/4 * a^2

a) P= area of incircle / area of triangle

b)P' = 1 - P
  • -1
What are you looking for?