Kai cuts out all the page numbers of a book. He takes each number and cuts the numbers into separate digits (single digit numbers are already separate). Given that the book has 999 pages numbered 1 through 999, if he chooses one of these digits at random, what is the probability it is a 7?

Is the answer 100/2889?

ANotSmartPerson Nov 15, 2018

#1**+3 **

Here are the distributions of ALL numbers from 1 to 999:

(0=189, 1=300, 2=300, 3=300, 4=300, 5=300, 6=300, 7=300, 8=300, 9=300)

Total = 2889. So, the probability that it is a 7 is:

**300/2,889=100/963 =~10.38%**

Guest Nov 15, 2018

#2**+3 **

Thanks, guest.....!!!

Here's a way to analyze this

We have 9 one-digit numbers = 9

And [ 99 - 10 + 1 ] = 90 two-digit numbers = 180 digits

And [ 999 - 100 + 1] = 900 three-digit numbers = 2700 digits

So.....the total number of digits is 9 + 180 + 2700 = 2889

The digit "7" will appear 10 times in each hundred in the units place = 10 * 10 = 100

And it will appear 10 times in each hundred n the tens place = 10 * 10 = 100

And it will appear 100 times from 700 - 799 in the hundreds place

So......the probability is

[ 100 + 100 + 100 ] / 2889 = 300 / 2889

CPhill Nov 15, 2018