"the life length x (in years) of a dvd player" is exponentially distributed with mean 5 years. what is the probability that a more than 5-year old dvd would still work for more than 3 years?

The exponential distribution is:

where 

The probability we want is how likely will a dvd player last more than 8 years, given it has already lasted 5 years
To find this, you use conditional probability.

where A is P(x>8) and B is P(x>5)
To find these probabilities, integrate over the distribution:


Sub into conditional probability formula:



Final Given a dvd player is more than 5 years old, the probability that it will last another 3 more years is about 54.9%