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  1. Chapter 13 Class 12 Probability
  2. Serial order wise

Transcript

Ex 13.5, 10 A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1/100 . What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice?Let X : Number of times he wins a prize Winning a prize on lottery is a Bernoulli trial So, X has a binomial distribution P(X = x) = nCx ๐’’^(๐’โˆ’๐’™) ๐’‘^๐’™ Here, n = number of lotteries = 50 Let X : Number of times he wins a prize Winning a prize on lottery is a Bernoulli trial So, X has a binomial distribution P(X = x) = nCx ๐’’^(๐’โˆ’๐’™) ๐’‘^๐’™ Here, n = number of lotteries = 50 p = Probability of winning a prize = 1/100 q = 1 โ€“ p = 1 โˆ’ 1/100 = 99/100 Hence, P(X = x) = 50Cx (๐Ÿ/๐Ÿ๐ŸŽ๐ŸŽ)^๐’™ (๐Ÿ—๐Ÿ—/๐Ÿ๐ŸŽ๐ŸŽ)^(๐Ÿ“๐ŸŽโˆ’๐’™) (a) Probability that he wins the lottery atleast once P (at least once) = P(X โ‰ฅ 1) = 1 โˆ’ P (0) = 1 โˆ’ 50C0 (1/100)^0 (99/100)^(50โˆ’0) = 1 โˆ’ 1 ร— 1 ร— (99/100)^50 = 1 โˆ’ (99/100)^50 (b) Probability that he wins the lottery exactly once P (exactly once) = P(X = 1) = 50C1 (1/100)^1 (99/100)^(50โˆ’1) = 50 ร— 1/100 ร— (99/100)^49 = 1/2 (99/100)^49 (c) Probability that he wins the lottery atleast twice P (atleast twice) = P(X โ‰ฅ 2) = 1 โ€“ [P(X = 0) + P(X = 1)] = 1 โ€“ ["50C0 " (1/100)^0 (99/100)^(50โˆ’0) "+ 50C1 " (1/100)^1 (99/100)^(50โˆ’1) ] = 1 โ€“ [(99/100)^50 "+" 1/2 (99/100)^49 ] = 1 โ€“ (99/100)^49 [99/100 "+" 1/2] = 1 โ€“ (99/100)^49 [(99 + 50)/100] = 1 โˆ’ 149/100 (99/100)^49

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.