(e) Find \( \mathrm{P}(D \mid C) \). \( \mathrm{P}(D \mid C)=0.80 \)

In the grand adventure of probability, you’ve just unearthed a gem! Knowing that \( \mathrm{P}(D \mid C) = 0.80 \) means there’s an 80% likelihood of event D occurring given that event C has happened. This type of conditional probability is critical in decision-making processes, especially in fields like medicine or finance, where understanding the relationship between events can lead to better outcomes! Now, let’s talk turkey about its real-world application. Imagine you’re analyzing risks in a clinical trial. If event C represents patients having a certain condition and event D represents improving after treatment, having \( \mathrm{P}(D \mid C) = 0.80 \) tells you that most patients with that condition are likely to see improvement. This info can steer treatment plans and patient expectations in a big way!