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

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 ?

• The probability all $100000$ parts last $7$ years? Very very small. There is only a $0.1\%$ chance they will all last $6$ hours – Henry Jul 12 at 10:01
• @Henry, thanks, could you please explain with solution? – dtc348 Jul 12 at 10:31

$$P(\text{all parts make it}) = \prod_{p\in\text{all products}}\exp(-m\cdot7) = \exp(-m\cdot 7)^{100000}$$
It's just the number you have, 0.49, multiplied with itself 100000 times, $$0.49\cdot0.49\cdot\ \dots\ \cdot0.49$$.
• Result is 0, if $0.49^{100000}$ – dtc348 Jul 12 at 10:36