# You have the numbers 1-24 written on a slip of paper. If you chose one slip at random what is the probability that you will not select a number which is divisible by 6?

##### 1 Answer

The probability is

#### Explanation:

Let A be the event of selecting a number divisible by 6 and B be the event of selecting a number not divisible by 6:

In general, if you have n slips of paper numbered 1 to N (where N is a big positive integer say 100) the probability of selecting a number divisible by 6 is ~1/6 and if N is exactly divisible by 6, then the probability is exactly 1/6

i.e.

if N is not divisible exactly by 6 then you would calculate the remainder, for example if N = 45:

(6*7 = 42, 45-42 = 3, the remainder is 3)

The greatest number less than N that is divisible by 6 is 42,

and

and they would be

if you instead chose 24 there would be 4: and they would be 6*1,6*2, 6*3,6*4 = 6,12,18,24

Thus the probability of choosing a number divisible by 6 between 1 and 45 is

and the probability of choosing a number not divisible by 6 would be the complement of that which is given by

For 1 to 45 it would be:

For 1 to 24 it would be: