$3.(10$ points$)$ A factory is known for producing $40\%$ defective products. As such, the manager is offering a $$buy one get one free$$ deal to their customers. The product is sold at $$10$ per unit and costs $$5$ to make and ship. Assume that the customer must receive at least one good product. Calculate the following.

$($a$)$ P$($customer will receive at least one good product on the first shipment$)$

$($b$)$ P$($customer will receive the first good product on the fourth shipment$)$

$($c$)$ The expected gain or loss per product sale.