Please Math Geniuses!!! Help with probability, Statistics?

Question

A study of Brand D washing machines that failed within three years (warranty period) was 28.7%. Of those that failed, 85.02% lasted over two years. What is the probability that a washer, which lasts at least two years, will still fail before the end of the warranty period?

Answer 1

Let X be the amount of time before failure, in years.
Given: P(X < 3) = 0.287
P(X >=2 | X < 3) = 0.8502

We know
P(X >= 2 | X < 3) = P(X >= 2 and X < 3) / P(X < 3)
So P(X >= 2 and X < 3) = P(X >= 2 | X < 3) . P(X < 3)
= 0.8502 (0.287) = 0.2440

So P(X < 2) = P(X < 3) - P(X >= 2 and X < 3) = 0.287 - 0.2440 = 0.0430
and hence P(X >= 2) = 1 - 0.0430 = 0.9570.

P(X < 3 | X >= 2) = P(X >= 2 and X < 3) / P(X >= 2)
= 0.2440 / 0.9570
= 0.255
So the probability that a washer that has lasted at least 2 years will still fail before the end of the warranty period is 25.5%.