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avatar+1351 

Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $248,$ $249,$ $250.$

 

(a) How many digits did Sam write, in total?

(b) Sam chooses one of the digits written down at random.  What is the probability that Sam chooses a $2$?

 Apr 23, 2024
 #1
avatar+128794 
+1

(a)

9 + 90*2  + 151 * 3  =  642  digits

 

 

(b)  Prob of 2   =

 

No. of 2's

 

In the ones place

10 in the first hundred

10 in the second hundred

5 in last 50

= 25

 

In the tens place

10 in the first hundred

10 in the second hundred

10 in the last 50

= 30

 

In the hundreds place

51  in  the last 51

 

Total 2's  = [ 25 + 30 + 51  ]  =  106

 

Prob of a 2  =  106  /  642  =    53  /  321

 

cool cool cool

 Apr 23, 2024

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