How would I solve this probability problem?

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enter image description here I'm trying to solve this problem for couple of days but can't seem to figure it out. Can someone let me know if I'm even going in the right direction? Thanks in advance

This what I have so far

|L ∩ T| U A ≤ 100
|L ∩ T| + |A| - |L ∩ T ∩ A| ≤ 100
115 - |L ∩ T ∩ A| ≤ 100
- |L ∩ T ∩ A| ≤ -15
|L ∩ T ∩ A| ≥ 15