Total number of tickets sold = 10,000
Number prizes awarded = 10
(i) If we buy one ticket, then
P (getting a prize) = 10/10000=1/1000
∴ P (not getting a prize) = 1-1/1000 = 999/1000
(ii) If we buy two tickets, then
Number of tickets not awarded = 10,000 − 10 = 9990
P (not getting a prize) = 9990C2 / 10000C2
(iii) If we buy 10 tickets, then
P (not getting a prize) = 9990C10 / 10000C10