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Misc 4 - In a lottery 10,000 tickets are sold, ten prizes - Using permutation

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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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 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﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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