(Solved): 3. ( 6 marks) Food delivery companies often classify orders as either "nearby" or "long-distance". ...

3. ( 6 marks) Food delivery companies often classify orders as either "nearby" or "long-distance". A food delivery company claims that a nearby order is delivered within 35 minutes with probability \( 0.7 \), and a long-distance order is delivered within 35 minutes with probability \( 0.25 \). Suppose that \( 78 \% \) of the orders are nearby order. (a) What is the probability that a randomly selected order is delivered within 35 minutes? (b) Given that a randomly selected order is more than 35 minutes, what is the probability that it is a nearby order?