Mathematics

Problem

If the probability that the random variable

X

takes the value

x

is given by

P(X = x) = k(x + 1)3^{-x}

x = 0, 1, 2, 3, \dots

, where

k

is a constant, then

P(X \ge 3)

is equal to (1)

\frac{7}{27}

(2)

\frac{4}{9}

(3)

\frac{8}{27}

(4)

\frac{1}{9}