Probability

So my professor did a problem on the board. Below I showed how he approached the problem and his solution. However, his handwriting really sucks. Please show the answer and the calculations required to get each answer so I can prepare for my exam. If my professor made a mistake, please mention it. Thanks

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3 programmers : A, B, C. Bugs in program . Programmer A : Finishes usually 75% of the problems he's been given. Programmer B: Finishes usually 65% or problems he's been given. Programmer C: Finishes 50 % of problems he's been given. They're working independently . What are the chances A & B independently will find the problem? What is the chance that A and B won't find the problem? What is the chance C will find the problem? What is the chance that none will find the problem? P (A U B U C)= ?

Professor's work but not sure:

A is 1 -.75

B is 1 -.65

A & B won't find the problem is (1 - both won't find the problem) = 0.125

C is 1 -.05

Chance that none find it: 1 -(1-A) (1-B)(1-C) = .95625

P (A U B U C) = 1 -(1-p(A) 1 - p(B) 1- p(C) = ??

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