If sample space contains infinite number of points then with the help of geometry that is length, area, volume many problems of probibility can be solved
For example : A point is selected randomely inside the circle then the probability that it is nearer to centre then its circumeference
Probability = 
= 
= 
(i) A sphere is circumscribed over a cube. Find the probability that a point lies inside the sphere, lies outside the cube.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)a 
Diagonal A D will be diameter of sphere. AD 2 = AC 2 + DC 2 = a 2 + a 2 + a 2 = 3a 2 ⇒ AD = 
a
Volume of sphere is 
π 
Volume of cube = a 3
Eequired probability = 1 – 
= 1 – 
(ii)a 20 2 – 12 2 = x 2 ⇒ x 2 = 400 – 144
x = 
= 16 ; P = 
(iii)c 0 < x < 10 x 2 + y 2 < 100
0 < y < 10
p = = 
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