For a geometric experiment involving \(n\) trials and an event that occurs with probability \(p\), the probability that the event of interest will occur in the first trial is \(p\). If it fails in the first trial but succeeds in the second, the probability of this occurring would be \((1-p)p\). If the first two trials fail but the third succeeds, the probability of this happening is \((1-p)^2p\). And so on.
The unfolding pattern suggests that the probability of success in the \(k\)th trial is \((1-p)^{k-1}p\), where \(1\le k\le n\).
This means the probability of this event happening by the 9th trial is
\((1-0.16)^{9-1}\times0.16\approx0.0397\)
