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?

Answer 1

Total number of tickets sold $=10,000$
Number prizes awarded $=10$
(i) If we buy one ticket
$P$ (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
Number of tickets not awarded $=10,000-10=9990$
$P$ (not getting a prize) $=$ $\frac{{9990}_{C_2}}{{10000}_{C_2}}$

(iii) If we buy 10 tickets then
$P$ (not getting a prize)$=$ $\frac{{9990}_{C_{10}}}{{10000}_{C_{10}}}$