If X_1 ,X_2 , …X_n are n independent events such that P (X_r ) = 1r+1 ,r=1 ,2 , … ,n, then the probability that none of the n events occur is

Question

Accepted Answer

Correct answer: B. (b) P (X_1^ ' ∩X_2^ ' ∩X_3^ ' … ∩X_n^ ' ) =P (X_1^ ' )P (X_2^ ' )P (X_3^ ' ) …P (X_n^ ' ) =(1- 12)(1- 13)(1- 14) …(1- 1n)(1- 1n+1) = 12 23 34 … … . n-1n nn+1= 1n+1

$If X_{1}, X_{2}, \dots X_{n} are n independent events such that P (X_{r}) = \frac{1}{r + 1}, r = 1, 2, \dots, n, then the probability that none of the n events occur is$

Solution

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