# Ex 13.5, 10 - Chapter 13 Class 12 Probability

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

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 1100 . 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 𝒒𝒏−𝒙 𝒑𝒙 n = number of lotteries = 50 p = Probability of winning a prize = 1100 q = 1 – p = 1 − 1100 = 99100 Hence, ⇒ P(X = x) = 50Cx 𝟏𝟏𝟎𝟎𝒙 𝟗𝟗𝟏𝟎𝟎𝟓𝟎−𝒙 (a) Probability that he wins the lottery atleast once P (at least once) = P(X ≥ 1) = 1 − P (0) = 1 − 50C0 11000 9910050−0 = 1 − 1 × 1 × 9910050 = 1 − 9910050 (b) Probability that he wins the lottery exactly once P (exactly once) = P(X = 1) = 50C1 11001 9910050−1 = 50 × 1100 × 9910049 = 12 9910049 (c) Probability that he wins the lottery atleast twice P (atleast twice) = P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 50C0 11000 9910050−0+ 50C1 11001 9910050−1 = 1 – 9910050+ 12 9910049 = 1 – 9910049 99100+ 12 = 1 – 9910049 99 + 50100 = 1 − 149100 9910049

Chapter 13 Class 12 Probability

Serial order wise

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