You own a pottery business that sells beautiful kiln fired mugs. You have classified customers at your online pottery store as either: 

Loyalty program members (20% of all customers), regular shoppers (60% of all customers), or occasional shoppers (20% of all customers).

When you have a new batch of mugs for sale you've found that 70% of loyalty programme members will buy a mug, 30% of regular shoppers buy a mug and 10% of occasional shoppers buy a mug. Mugs are sold for $30 each but loyalty programme members get a discount of $5.

1. What proportion of customers will purchase a mug?
   
    Given that someone buys a mug what is the probability that they are a member of the loyalty program? Show your working.
   
    What is the average revenue per customer for a new batch of mugs?  (NB Remember to include customers who don't buy a mug in your calculations.)