Question

an integer is chosen at random fro the first two hundred digits. what is the probability that the integer chosen is divisible by 6 0r 8?

Answer 1

so the number divisible by 6 , 8 must also be divisible with 24 

so the smallest number divisible by 24 is 24 and the highest number is 192 

so the number of digits is 192 = 24 + (n-1)24 

⇒168/24 + 1 = n 

⇒ n = 8 so the 

probability of that the integer chosen is divisible by 6 or 8 is 8 / 200 = 1/25 = 0.04

Answer 2

The no.s are divisible by either 6 or 8
If the digits are divisible 6 they are multiples of 6.
             We have 200/6=33.3  i.e 33 digits which are divisible by 6.
Similarly we have 200/8=25  i.e 25 digits divisible by 8.
There are some common integer which are also divisible by 6 and 8.
We have LCM of 6&8 is 24
So the digits divisible by 24 are both divsisible by 6 & 8.
200/24= 8.3  i.e 8 digits are divisible by 6 and 8
We have no. of digits divisible either by 6 or 8 = 33+25-8=50
hence the probability is 50/200 i.e 1/4