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Question: How to verify this probability?

Question:How to verify this probability?

Markiyan Hirnyk 7759 Maple
statistics probability
February 04 2018
0

I mean the following Maple 2017.3 result

restart; with(Statistics):
X := RandomVariable(Geometric(1/3)):
Probability(sin(X) <= 1/2);
                            2839595/4782969

Mma 11.2 fails with it. It's unclear for me how Maple calculates the above result. Trying printlevel:=10:, I don't understand much. Also the result

solve({x >= 0, sin(x) <= 1/2}, [x], AllSolutions);
Warning, solutions may have been lost
  
[[x <= (1/6)*Pi, 0 <= x], [x <= 13*Pi*(1/6), 5*Pi*(1/6) <= x], [x <= 25*Pi*(1/6), 17*Pi*(1/6) <= x],
 [x = 29*Pi*(1/6)]]

does not encourage.
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