If the probability that the random variable \(X\) takes the value \(x\) is given by \(\mathrm{P}(\mathrm{X}=\mathrm{x})=\mathrm{k}(\mathrm{x}+1){3}^{-\mathrm{x}}\), \(\mathrm{x}=0,1,2,3\ldots ..\), where \(k\) is a constant, then \(P\left(X\geq 3\right)\) is equal to

[JEE Main 2025, 3 Apr (Shift 2)]

Question

If the probability that the random variable \(X\) takes the value \(x\) is given by \(\mathrm{P}(\mathrm{X}=\mathrm{x})=\mathrm{k}(\mathrm{x}+1){3}^{-\mathrm{x}}\), \(\mathrm{x}=0,1,2,3\ldots ..\), where \(k\) is a constant, then \(P\left(X\geq 3\right)\) is equal to

[JEE Main 2025, 3 Apr (Shift 2)]

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