Question:
In a certain lottery, 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy
(a) one ticket
(b) two tickets
(c) 10 tickets?
Solution:
Total number of tickets sold = 10,000
Number prizes awarded = 10
(i) If we buy one ticket, then
$P$ (getting a prize) $=\frac{10}{10000}=\frac{1}{1000}$
$\therefore P($ not getting a prize $)=1-\frac{1}{1000}=\frac{999}{1000}$
(ii) If we buy two tickets, then
Number of tickets not awarded = 10,000 − 10 = 9990
$\mathrm{P}$ (not getting a prize) $=\frac{{ }^{9990} \mathrm{C}_{2}}{{ }^{10000} \mathrm{C}_{2}}$
(iii) If we buy 10 tickets, then
$P$ (not getting a prize) $=\frac{{ }^{9990} \mathrm{C}_{10}}{{ }^{10000} \mathrm{C}_{10}}$