(Solved): 2. [ \( \mathbf{5} \) marks] A detective is investigating a case in a town where \( 30 \% \) of res ...

2. [ \( \mathbf{5} \) marks] A detective is investigating a case in a town where \( 30 \% \) of residents own red cars. A witness claims to have seen a red car fleeing the scene of a crime. However, the witness is known to correctly identify car colors only \( 80 \% \) of the time. What is the probability that a red car was actually involved, given that the witness reported seeing a red car?