# Misc 9

Last updated at March 20, 2017 by Teachoo

Last updated at March 20, 2017 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 n = number of trials = 6 p = Probability of success q = Probability of failure = 1 – p Given experiment succeeds twice as often it fails So, p = 2q p = 2(1 – p) p = 2(1 – p) p = 2 – 2p 3p = 2 p = 𝟐𝟑, Hence, q = 1 – p = 1 – 23 = 13 Hence, P(X = x) = 6Cx 𝟐𝟑𝒙 𝟏𝟑𝟔−𝒙 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 234 136−4+6C5 235 136−5+6C6 236 136−6 = 6C4 234 132+6C5 235 131+6C6 236 130 = 15 × 234 132+6 235 131+1 236 × 1 = 234 15 × 132+6 23 13+ 232 = 234 159+ 129+ 49 = 𝟑𝟏𝟗 𝟐𝟑𝟒

Example 7
Important

Example 6 Important

Ex 13.1, 10 Important

Ex 13.1, 12 Important

Example 11 Important

Ex 13.2, 7 Important

Ex 13.2, 11 Important

Ex 13.2, 14 Important

Example 17 Important

Example 18 Important

Example 20 Important

Example 21 Important

Ex 13.3, 2 Important

Ex 13.3, 4 Important

Ex 13.3, 8 Important

Ex 13.3, 10 Important

Ex 13.3, 12 Important

Ex 13.3, 13 Important

Example 25 Important

Example 26 Important

Example 27 Important

Example 28 Important

Example 29 Important

Ex 13.4, 3 Important

Ex 13.4, 6 Important

Ex 13.4, 11 Important

Ex 13.4, 15 Important

Example 31 Important

Example 32 Important

Ex 13.5, 4 Important

Ex 13.5, 6 Important

Ex 13.5, 10 Important

Ex 13.5, 13 Important

Example 35 Important

Example 36 Important

Misc 6 Important

Misc 9 Important You are here

Misc 11 Important

Misc 13 Important

Misc 16 Important

Class 12

Important Question for exams Class 12

- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
- Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.