Bayesian inference in practice: marketing campaign evaluation (part 1)

For the past 5.5 years I have been working mostly in customer/marketing analytics departments. A common task is the evaluation of marketing campaigns, for example:

Split a homogeneous group of customers (e.g., ‘new’) into 2 groups, A & B
Send group A an email with a €10,- coupon
Send group B the same email without the €10,- coupon