You purchase a new motor vehicle and are considering purchasing an extended bumper-to-bumber warranty. The extended warranty adds 3 years of protection to the basic warranty and costs $3,000. The following probability distribution shows the anticipated repair costs and associated probabilities during the extended warranty's 3 additional years of protection:
| REPAIR COSTS | PROBABILITY |
| $10,000 |
0.10 |
| $5,000 |
0.20 |
| $2,000 |
0.45 |
| $1,000 |
0.25 |
Should you purchase the extended warranty? Please show reasoning/how you came up with your answer!