sample space of a number being a natural number from 1 to 100.
A natural number is selected at random from 1 to 100. Find the probability of
(a) getting a multiple of 4,
Sample space:
S = {1,2,3,4,5,6,7,8,9,10,11,12,...,95,96,97,98,99,100}
Event of a number being a natural number which is a multiple of 4.
E1 = {4,8,12,16,20,24,28,32,36,40,...,80,84,88,92,96,100}
There are 100 members of the sample space.
There are 25 members of the event E1.
{You can tell there are 25 in E1 by observing that if you divided them all
by 4 you'd have the numbers from 1 through 25.]
Answer 25 out of 100 = 25/100 which reduces to 1/4.
(b) getting a number that is not a multiple of 4.
The sample space is the same:
S = {1,2,3,4,5,6,7,8,9,10,11,12,...,95,96,97,98,99,100}
E2 = {1,2,3,5,6,7,9,10,11,13,...,95,97,98,99}
There are 100 members of the sample space.
There are 75 members of the event E1.
{You can tell there are 75 in E2 by subtracting 100-25 = 75]
Answer 75 out of 100 = 75/100 which reduces to 3/4.
Notice that E2 is the complement event of E1, so
another way to do part (b) is to subtract the probability of E1 from
1. 1 - 1/4 = 3/4.
Edwin
