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?
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%
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