CBSE Class 12 Sample Paper for 2025 Boards

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Question 31 (B) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 13, 2024 by

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Question 31 (B) A random variable 𝑋 can take all non - negative integral values and the probability that 𝑋 takes the value π‘Ÿ is proportional to 5^(βˆ’π‘Ÿ). Find 𝑃(𝑋<3).It’s given that P(X = r) is proportional to 5^(βˆ’π‘Ÿ) i.e. P(X = r) ∝ 5^(βˆ’π‘Ÿ) So, we can write P(X = r) = k 5^(βˆ’π‘Ÿ) = π’Œ/πŸ“^𝒓 Where k is some constant Thus, 𝑷(𝒓=𝟎)=π‘˜/5^0 = π‘˜/1 = π’Œ 𝑷(𝒓=𝟏)=π‘˜/5^1 = π’Œ/πŸ“ 𝑷(𝒓=𝟐)=π‘˜/5^2 𝑷(𝒓=πŸ‘)=π‘˜/5^3 First term = a = 1 Common ratio = r = (1/5)/1=𝟏/πŸ“ Now, Sum of infinite GP = π‘Ž/(1 βˆ’ π‘Ÿ) = 1/(1 βˆ’ 1/5) = 1/(4/5) = πŸ“/πŸ’ Now, π’Œ(𝟏+𝟏/πŸ“+𝟏/πŸ“^𝟐 +𝟏/πŸ“^πŸ‘ +…)=𝟏 Putting values π‘˜ Γ—5/4=1 π’Œ=πŸ’/πŸ“ We need to find 𝑃(𝑋<3). Thus, 𝑷(𝑿<πŸ‘)=𝑃(0)+𝑃(1)+𝑃(2) =π’Œ+π’Œ/πŸ“+π’Œ/πŸ“^𝟐 =π‘˜(1+1/5+1/5^2 ) =π‘˜(1+1/5+1/25) =π‘˜((25 + 5 + 1)/25) =π‘˜ Γ—31/25 Putting π’Œ=πŸ’/πŸ“ =4/5 Γ—31/25 =πŸπŸπŸ’/πŸπŸπŸ“

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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo