Suppose X has an exponential distribution with mean 25 Calc

Suppose X has an exponential distribution with mean = 25. Calculate P(X < 30|X > 10). (Hint: apply the memoryless property)

Mean = 1/lambda = 25

So lambda = 1/25

P(X>10) = 1 - P(X<10) = 1 - (1-e^(-lambda*10)) = e^(-10/25) = e^(-2/5) = 0.6703

P(10<X<30) = P(X<30) - P(X<10) = (1-e^(-lambda*30)) - (1-e^(-lambda*10)) = e^(-10/25) - e^(-30/25) = 0.3691

P(X<30|X>10) = P(10<X<30)/P(X>10) = 0.3691/0.6703 = 0.55067