# Ex 13.4, 15 - Chapter 13 Class 12 Probability (Term 2)

Last updated at Feb. 10, 2020 by Teachoo

Ex 13.4

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Ex 13.4, 10 Deleted for CBSE Board 2022 Exams

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Ex 13.4, 15 Deleted for CBSE Board 2022 Exams You are here

Ex 13.4, 16 (MCQ) Deleted for CBSE Board 2022 Exams

Ex 13.4, 17 (MCQ) Important Deleted for CBSE Board 2022 Exams

Chapter 13 Class 12 Probability (Term 2)

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Ex 13.4, 15 In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var (X). Given that X = 0 is Members oppose X = 1 is members favour proposal Given, 70% of members favour proposal So, P(X = 1) = 70% = 0.7 and 30% of members oppose proposal So, P(X = 0) = 30% = 0.3 ∴ Probability distribution is The expectation value E(x) is given by : E 𝑿 = 𝑖 = 1𝑛𝑥𝑖𝑝𝑖 = 0 × 0.3 + 1 × 0.7 = 0.7 The variance of x is given by : Var 𝑋=𝐸 𝑋2− 𝐸 𝑋2 So, finding 𝐸 𝑋2 E 𝑿𝟐= 𝑖 = 1𝑛 𝑥𝑖2𝑝𝑖 = 02 × 0.3 + 12 × 0.7 = 0 + 0.7 = 0.7 Now, Var 𝒙 = 𝐸 𝑥2− 𝐸 𝑥2 = 0.7 – 0.72 = 0.7 1−0.7 = 0.7 0.3 = 0.21 Hence the expectation E(x) = 0.7 & variance var(x) = 0.21