+2653 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 $2$?
+129885 (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
