Probability question..how to set up? A battery company sells their batteries in packages of 5. They have a special guarantee on their 5 packs. If one of the 5 is a dud, the customer gets their money back. If 2 of the batteries is a dud they get double their money back. If 3 or more of the batteries is a dud they get triple their money back. Suppose 5% of the batteries are duds and whether any one batter is a dud is independent of whether any other battery is a dud. Supposed the company charges three dollars for a 5 pack. What is their expected income per pack taking into account the customers who get money back due to duds? Can anyone give me any tips on how to set this up? I don't know what the random variable I'm supposed to focus on is. Probability is not my strength...

Calculate the chance of $0,1,2$ duds from the binomial distribution You get 3 from a pack with no duds, 0 from the ones with one dud, -3 from the ones with two, and -6 from the rest.