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