Independent solution

How to solve this Exponential Distribution question

Setup

Setup

Let S(t) denote the exponential survival function.

S(t)=e−λtS(t)=e^{-\lambda t}

Model

Model

By memorylessness, conditioning on survival to the initial time leaves only the additional duration.

Pr⁡(X>15∣X>5)=S(10)=0.027\Pr(X>15\mid X>5)=S(10)=0.027
Pr⁡(X>25∣X>5)=S(20)\Pr(X>25\mid X>5)=S(20)

Compute

Compute

Exponential survival over twenty units is the square of survival over ten units.

S(20)=S(10)2=(0.027)2=0.000729S(20)=S(10)^2=(0.027)^2=0.000729

Answer

Answer

The probability rounds to 0.0007.

0.0007(A)\boxed{0.0007\quad\text{(A)}}