S1 Geometric distribution

[DelBoy]

Stuck on this. Any help plz

The random variable S can take the values 1,2,3,... and has a geometric distribution. It is given that P(S=2) = 0.2244. Find the value of P(S=1), given that it is less than 0.5.

[Unregistered]

For a Geometric distribution p(S=n) = (1-p)^(n-1)*p

Hence
p(S=2) = 0.2244
implies (1 - p)*p = 0.2244
and so p^2 - p + 0.2244 = 0
(p - 0.66)(p - 0.34) = 0
p = 0.66 or p = 0.34
But p<0.5
so p=0.34

and p(S=1) = p = 0.34

[DelBoy]

Your brilliant!