# Probability of 100,000 Computer parts, if one computer part lasts more than seven years is $0.4966$

by dtc348   Last Updated July 12, 2019 09:19 AM - source

If the length of time the computer part lasts is exponentially distributed with mean value is $$10$$.

So, for the exponential distribution, we can find the probability of one computer parts.

$$p(x>7) = e^{(-m * 7)} = 0.4966$$ where $$m = \frac{1}{mean} = 0.1$$.

My question, what is probability of $$100000$$ computer parts lasts more than seven years ?

Tags :

Assuming their lifespan is independepent, and they are all exponentially distributed like you say,

$$P(\text{all parts make it}) = \prod_{p\in\text{all products}}\exp(-m\cdot7) = \exp(-m\cdot 7)^{100000}$$

First step is independence, second step is rewriting the same thing.

It's just the number you have, 0.49, multiplied with itself 100000 times, $$0.49\cdot0.49\cdot\ \dots\ \cdot0.49$$.

Gijs
July 12, 2019 08:44 AM