# 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?

2
by hthomasgangte

2015-01-09T15:50:43+05:30

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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
hope it helps
plz mark as best
2015-01-09T17:25:42+05:30
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