Question

What is the probability that a number between 1 and 200 is divisible by neither 2, 3,?

Answer 1

A)numbers divisible by 2: 2002=1002002=100
B)numbers divisible by 3: 2003=662003=66
C)numbers divisible by 5: 2005=402005=40
counting twice

AB)numbers divisible by 6: 2006=332006=33
AC)numbers divisible by 10: 20010=2020010=20
BC)numbers divisible by 15: 20015=1320015=13
counting 3 times

ABC)numbers divisible by 30: 20030=620030=6
Total of numbers = A + B + C - AB - AC - BC + ABC = 100 + 66 + 40 - 33 - 20 - 13 + 6 = 146

Answer 2

Let total no b/w 1 to 200 = 198
S be the sample space {2,3,4,5,6,7,_____,199}
n(S) = 198
Let E denote the no• which divisible by 2,3 = {5,7,11,13,17,19,23,25,29,31,35,37,41,43,47,49,53,55,59,61,65,67,71,73,77,79,83,85,89,91,95,97,101,103,107,109,113,115,119,121,125,127,131,133,137,139,143,145,149,151,155,157,161,163,167,169,173,175,179,181,185,187,191,193,197,199}=66
n(E)= 66
P(E) = n(E)/n(S)
= 66/198 =1/3