If the probability that the random variable X takes values x is given by P(X=x)=k(x+1) 3⁻ˣ, x=0,1,2,3,, where k is a constant, then P(X ≥ 2) is equal to:

Statistics and Probability: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q5006

JEE Main 20238 Apr, Evening shiftMathematicsMediumStatistics and Probability258× since 2002

If the probability that the random variable

\mathrm{X}

takes values

x

is given by

\mathrm{P}(\mathrm{X}=x)=\mathrm{k}(x+1) 3^{-x}, x=0,1,2,3, \ldots

, where

\mathrm{k}

is a constant, then

\mathrm{P}(\mathrm{X} \geq 2)

is equal to :