2. a) There are 10000 - 1000 + 1 = 9001 numbers between and including 1000 and 10000.
Since 1000 = 4 · 250 and 10000 = 4 · 2500, the
number of integers between and including 1000 and 10000 which are divisible by 4 is the
same as the number of integers in the list of integers from 250 to 2500, namely 2500 - 250 + 1 = 2251. Note that this is slightly more than 1/4 of the integers in the original
list.
b) If S is our sample space and E is the event
that a number is divisible by 4, then from part a) we know that n(S) = 9001, and n(E) =
2251 , so
P(E) = n(E) / n(S) = 2251 / 9001.