\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(X\) be a random variable following a geometric distribution with parameter \(p = 0.4\).
Calculate the following probabilities, rounding your results to three decimal places:
  1. \(P_{X>3}(X > 10) = \)
  2. \(P_{X>8}(X \geq 12) = \)
  3. \(P_{X>2}(X \leq 4) = \)
  4. \(P_{X>5}(X < 11) = \)