An electronics retailer offers an optional protection plan for a mobile phone it sells. Customers can choose to buy the protection plan for

$\backslash [\backslash$$$100\backslash ],$ and in case of an accident, the customer pays a

$\backslash [\backslash$$$50\backslash ]$ deductible and the retailer will cover the rest of the cost of that repair. The typical cost to the retailer is

$\backslash [\backslash$$$200\backslash ]$ per repair, and the plan covers a maximum of

$\backslash [3\backslash ]$ repairs.

Let

$\backslash [$X$\backslash ]$ be the number of repairs a randomly chosen customer uses under the protection plan, and let

$\backslash [$F$\backslash ]$ be the retailer's profit from one of these protection plans. Based on data from all of its customers, here are the probability distributions of

$\backslash [$X$\backslash ]$ and

$\backslash [$F$\backslash ]$: