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 August 14, 2026 by

Question 31 (B) - A random variable X can take all non-negative - CBSE Class 12 Sample Paper for 2025 Boards

part 2 - Question 31 (B) - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12
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Transcript

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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