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AP EAMCET202318 May 2023Morning ShiftMathematicsProbabilityActual

If X ₁, X ₂, X _ n are n independent events such that P ( X _ r )= 1 r+1 , r=1,2, , n , then the probability that none of the n events occur is

Options

  1. A1 n
  2. B1 n+1
  3. Cn n +1
  4. Dn+1 n+2

Correct answer

B. 1 n+1

Step-by-step solution

P ( X ₁^ X ₂^ X ₃^ X _ n ^ ) aligned & =P (X₁^ ) P (X₂^ ) P (X₃^ ) P (X_n^ ) & = (1- 1 2 ) (1- 1 3 ) (1- 1 4 ) . (1- 1 n ) (1- 1 n+1 ) & = 1 2 2 3 3 4 n-1 n n n+1 = 1 n+1 aligned

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