Do the Math

A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold.
P(X = 0, Y = 0) = ¹ / ₆
P(X = 1, Y = 0) = ¹/₁₂
P(X = 1, Y = 1) = ¹ /₆
P(X = 2, Y = 0) = ¹ /₁₂
P(X = 2, Y = 1) = ¹ /₃
P(X = 2, Y = 2) = ¹/₆

What is the variance of X?

1. 0.47
2. 0.58
3. 0.83
4. 1.42
5. 2.58