Misc 4
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
Since, 1 ticket is chosen out of 10000 tickets
n(S) = 10000C1
= 10000!/1!9999! = (10000 × 9999!)/(1 × 9999!) = 10000
Now out of 10000 tickets only 10 have a prize
Hence number of tickets not having prize
= 10000 – 10
= 9990
Let A be the event that if we buy 1 ticket it does not have a prize
Hence this 1 ticket will be out of 9990 ticket
n(A) = 9990C1
= 9990!/1!(9990 − 1)! = 9990!/1!9989! = (9990 × 9989!)/(1 × 9989!) = 9990
Probability not getting a prize if we get one ticket = P(A)
= (𝑛(𝐴))/(𝑛(𝑆))
= 9990/10000
= 𝟗𝟗𝟗/𝟏𝟎𝟎𝟎
Misc 4
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
(B) Two tickets
2 ticket is chosen out of 10000 ticket
Hence n(S) = 10000C2
Let B be the event that if we buy two ticket it does not have a prize
Hence this 2 ticket will be out of 9990 ticket
n(B) = 9990C2
Thus,
P(B) = (𝑛(𝐵))/(𝑛(𝑆))
= 𝟗𝟗𝟗𝟎𝑪𝟐/𝟏𝟎𝟎𝟎𝟎𝑪𝟐
Misc 4
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
(c) 10 ticket
10 ticket is chosen out of 10000 ticket
Hence n(S) = 10000C10
Let C be the event that if we buy 10 tickets it does not have prize
Hence these 10 ticket will be out of 9990 ticket
So, n(C) = 9990C10
P(C) = (𝑛(𝐶))/(𝑛(𝑆)) = 𝟗𝟗𝟗𝟎𝑪𝟏𝟎/𝟏𝟎𝟎𝟎𝟎𝑪𝟏𝟎

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.