Imagine that United Airlines invests $45 million into a direct carbon capture technology firm in a plan to offset a portion of its future carbon emissions from burning jet fuel. If the plan is successful, in 2050, the firm will save $400 million in costs. If the plan is unsuccessful, the firm will face a cost increase of $25 million in 2050. Assume these costs are both one-time costs in 2050 - 30 years from now - and the interest rate is 3%. What is the minimum probability of success that would make this investment worthwhile? (Hint: The probability of failure is 1 minus the probability of success). Show your work.