+1418 Sam writes down the numbers $1,$ $2,$ $\dots,$ $315,$ $316,$ $317,$ $\dots,$ $249,$ $250.$
(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 $2$?
+129771 1-9 = 9 digits
10 - 99 = 180 digits
100 - 199 = 300 digits
200 - 250 = 151 digits
9 + 180 + 300 + 151 = 640 digits
No. of 2's
1-100 = 10 + 10 = 20
101 - 199 = 10 + 10 = 20
200 - 250 = 5 + 10 + 51 = 66
20 + 20 + 66 = 106
Prob of 2 = 106 / 640 = 53 / 320 (if I didn't mis-count !!! )
