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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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