First success on an even trial

EasyRandom Variables Expected Value~3m

Each trial succeeds independently with probability $0.2$ . What is the probability that your first success arrives on an even-numbered trial (trial $2$ , $4$ , $6$ , …)? Give a decimal to four places.

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Sum $P(X=2k)$ over $k=1,2,\dots$ - a geometric series in $q^2$ .
It collapses to $q/(1+q)$ with $q=0.8$ .

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0.4444 (± 0.001)

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Asked at: Game-Based Aptitude, Options Market-Making

First success on an even trial

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