Question 962258
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,
<pre>
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.

E<sub>1</sub> = {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 E<sub>1</sub>.  

{You can tell there are 25 in E<sub>1</sub> 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.
</pre>
(b) getting a number that is not a multiple of 4. 
<pre>
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}

E<sub>2</sub> = {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 E<sub>1</sub>.  

{You can tell there are 75 in E<sub>2</sub> by subtracting 100-25 = 75]

Answer 75 out of 100 = 75/100 which reduces to 3/4.

Notice that E<sub>2</sub> is the complement event of E<sub>1</sub>, so
another way to do part (b) is to subtract the probability of E<sub>1</sub> from
1.   1 - 1/4 = 3/4.

Edwin</pre>