Chapter 13 Class 12 Probability

Class 12
Important Questions for exams Class 12

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### Transcript

Question 6 A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?If a trial is Bernoulli, then There is finite number of trials They are independent Trial has 2 outcomes i.e. Probability success = P then Probability failure = q = 1 – P (4) Probability of success (p) is same for all trials Let X : be the number marked on bulb drawn Picking balls is a Bernoulli trial So, X has binomial distribution P(X = x) = nCx 𝒒^(𝒏−𝒙) 𝒑^𝒙 Here, n = number of times we pick the bulb = 4 p = Probability of getting digit 0 = 1/10 q = 1 – p = 1 – 1/10 = 9/10 Hence, P(X = x) = 4Cx (𝟏/𝟏𝟎)^𝒙 (𝟗/𝟏𝟎)^(𝟒−𝒙) We need to find Probability that none is marked with 0 i.e. P(X = 0) P(X = 0) = 4C0(1/10)^0 (9/10)^(4 −0) = (4 !)/((4 − 0) ! 0 !) ×1×(9/10)^4 = (4 !)/(4 !)×〖9 〗^4/〖10〗^( 4) = 〖9 〗^4/〖10〗^( 4) = (𝟗/𝟏𝟎)^𝟒

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#### Davneet Singh

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.