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) Ten tickets?

Answer 1

Total number of tickets sold $= 10,000$
Number prizes awarded $= 10$

(i) If we buy one ticket, then
P (getting a prize) $=\dfrac{10}{10000}=\dfrac{1}{1000}=\dfrac{10}{10000}=\dfrac{1}{1000}$

$∴P$ (not getting a prize) $=1-\dfrac{1}{1000}=\dfrac{999}{1000}$

(ii) If we buy two tickets, then
Number of tickets not awarded$= 10,000 - 10 = 9990$
P $$$(not getting a prize) =\dfrac{9990 C_2}{10000C_2}$

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