Basically the probability being asked is conditional probability :
P((2 <= x <= 3) | (x >= 2) ) meaning that it will break somewhere in the third year but we are given that the product is well till 2 years .The numerator term of probability can be written as :
P(2 <= x <= 3) ∩ (x >=2 )) = P(2 <= x <= 3 )
= P(x >= 2) - P(x >= 3)
= 1/e2/5 - 1/e3/5 (according to the given function for P(x >= t) = e-t/5)
= 0.1215
But we are given it works fine till 2 years .
So , P(x >= 2 ) = 1 / e0.4
= 0.6703
Therefore , P((2 <= x <= 3) | (x >= 2) ) = P(2 <= x <= 3) ∩ (x >=2 )) / P(x >= 2 )
= 0.1215 / 0.6703
= 0.181
Hence the required probability should be 0.181