A civil engineering company is working on three construction projects: a bridge $($Project A$),$ a highway $($Project B$),$ and a dam $($Project C$).$ Due to the challenging nature of these projects, the probability of encountering significant geological obstacles is non$-$negligible. The probabilities of encountering such obstacles for Projects A$,$ B$,$ and C are $0\mathrm{.}30,0\mathrm{.}25,$ and $0\mathrm{.}40,$ respectively.

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CE $210-$ Probability and Statistics Okan $$lhan

Furthermore, if a project encounters geological obstacles, the probability of a project delay is $0\mathrm{.}75.$ If a project does not encounter geological obstacles, the probability of a delay due to other factors $($like weather or logistical issues$)$ is $0\mathrm{.}10.$

One of the projects reports a delay. Given this information, what is the probability that the delayed project is Project $C,$ and the delay is due to geological obstacles?