# Ex 13.4, 11

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 by Teachoo

Transcript

Ex 13.4, 11(Method 1) Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X. Tossing a Die is a Bernoulli trial So, X has a binomial distribution P(X = x) = nCx 𝒒𝒏−𝒙 𝒑𝒙 Here, n = number of tosses of die = 2 p = Probability six appears = 16 q = 1 – p = 1 – 16 = 56 Hence, ⇒ P(X = x) = 2Cx 𝟏𝟔𝒙 𝟓𝟔𝟐 − 𝒙 Since pair of die are thrown, We can get 0 six, 1 six or 2 six So, X can be 0, 1 , 2 Putting values in (1) P(X = 0) = 2C0 160 562 −0 = 1 × 562 = 2536 P(X = 1) = 2C1 161 562 − 1 = 2 × 16 × 56 = 1036 P(X = 2) = 2C2 162 562 − 2 = 1 × 162 = 136 Thus, probability distribution is The Expectation of X is given by E(X) = 𝜇= 𝑖=1𝑛𝑥𝑖𝑝𝑖 = 0 × 2536+1 × 1036+2 × 136 = 1036+ 236 = 1236 = 𝟏𝟑 Ex 13.4, 11(Method 2) Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X. Let X be the number of sixes occur So, value of X can be 0, 1 or 2 Total number of possible outcomes = 36 S = (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) So, our probability distribution is The Expectation of X is given by E(X) = 𝜇= 𝑖=1𝑛𝑥𝑖𝑝𝑖 = 0 × 2536+1 × 1036+2 × 136 = 1036+ 236 = 1236 = 𝟏𝟑

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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.