Down Dog Yoga is a fitness studio which offers a variety of fitness classes such as yoga, Pilates

and Barre. On the first day of each month, customers have the option of pre-paying for classes

at a discounted rate of $10 per class. The purchased classes are loaded onto a smartphone

app. Upon entering the studio to take a class, the customers scan their phone to use up one of

the class credits pre-loaded on their app. If they come in for a class and have run out of credits

on their app, they can purchase access to a class for a price of $14 per class. If, on the other

hand, they reach the end of the month and still have some class credits, they receive a refund

for $5 per class credit remaining. The credit balance is then reset to zero on the first day of

each month for each customer.

On May 1st, Alice is trying to decide how many classes she wants to pre-pay for. Based on past

observations and her schedule for the month, she estimates she will be able to attend

between 0 and 10 classes over the course of the month, with the following table giving the

corresponding probability for each value: