# Misc 9 - Chapter 13 Class 12 Probability

Last updated at Feb. 15, 2020 by Teachoo

Last updated at Feb. 15, 2020 by Teachoo

Transcript

Misc 9 An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes. Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p Let X: Number of successes Since we are talking about success and failure It is a Bernoulli trial So, X has a binomial distribution Here, n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p We need to probability that there will be at least 4 successes i.e. P(X ≥ 4) P(X ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) = 6C4(2/3)^4 (1/3)^(6−4)+"6C5" (2/3)^5 (1/3)^(6−5)+"6C6" (2/3)^6 (1/3)^(6−6) = 6C4(2/3)^4 (1/3)^2+"6C5" (2/3)^5 (1/3)^1+"6C6" (2/3)^6 (1/3)^0 = 15 × (2/3)^4 (1/3)^2+"6" (2/3)^5 (1/3)^1+"1" (2/3)^6 × 1 = (2/3)^4 ("15 × " (1/3)^2+"6" (2/3)(1/3)+(2/3)^2 ) = (2/3)^4 (15/9+12/9+4/9) = 𝟑𝟏/𝟗 (𝟐/𝟑)^𝟒

Miscellaneous

Misc 1

Misc 2 Important

Misc 3

Misc 4 Deleted for CBSE Board 2021 Exams only

Misc 5 Important Deleted for CBSE Board 2021 Exams only

Misc 6 Important Deleted for CBSE Board 2021 Exams only

Misc 7 Important

Misc 8 Important

Misc 9 Important Deleted for CBSE Board 2021 Exams only You are here

Misc 10 Important

Misc 11 Important

Misc 12

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16 Important

Misc 17 Important

Misc 18

Misc 19

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.