An electrical switch has an exponential distribution with an average lifetime of 2 years. For a single system, what is the probability we can keep the switching mechanism operable for 10 years if we...

An electrical switch has an exponential distribution with an average lifetime of 2 years. For a single system, what is the probability we can keep the switching mechanism operable for 10 years if we assume we will have to replace a switch due to failures three times during the 10-year period? (Hint: Think Gamma Distribution)