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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
avatar
+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
avatar+92785 
+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

 

 

cool cool cool

CPhill  Nov 15, 2018
 #3
avatar+160 
+1

Thanks!

ANotSmartPerson  Nov 16, 2018

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