A number is randomly chosen from 1 to 100(both

Solution

Total numbers divisible by 2 = 100/2 = 50
Total numbers divisible by 3 = 100/3 = 33
Total numbers divisible by 5 = 100/5 = 20
Numbers that are multiples of 2 and 3, 3 and 5, 2 and 5 would have been added twice. So we need to subtract it.
Total numbers divisible by 2 and 3 = 100/6 = 16
Total numbers divisible by 3 and 5 = 100/15 = 6
Total numbers divisible by 2 and 5 = 100/10 = 10
We now need to add the number divisible by 2,3, and 5
LCM = 2 x 3 x 5 = 30
Total numbers divisible by 30 = 100/30 = 3
So numbers divisible by 2,3 or 5 = 50 + 33 + 20 - (16 + 6 + 10) + 3 = 103 - 32 + 3 = 74
Required probability = 74/100 = 37/50