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, 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