You first need to determine how much you owned when the house was purchased, half or one-third.
Next, was the transfer was a gift?
Your basis (cost) to use when the property is sold would be calculated on that amount. So if it was 155k and you owned half, your basis would start at 77,500. If you only owned one-third, it would be 51,667.
The portion they gifted you would be their adjusted basis, so the same as when purchased unless they made a major improvement.
So you would end up right where you started at, having a basis of 155,000.
If your parents sold the home, they could have claimed an exclusion for living there at least 2 of the last 5 years.
You won't be able to do that. You'll have to pay capital gains on anything over 155,000.
There also are many ways the deed could have transferred, which varies state to state. You might want to speak with a real estate attorney or accountant that is experienced with real estate in your state.
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