Stats-crv-exponential distribution

[schapman22]

Homework Statement

The time to failure for a certain light bulb in constant failure rate mode has a mean time to failure of 5000 hours.

What is the probability that a randomly chosen light bulb is still burning after 10,000 hours? Give answer to 4 decimals.

If 5 light bulbs are installed in different street lamps along Main Street, what is the probability that at least 1 will be working after 10,000 hours? Give answer to 4 decimals.

The Attempt at a Solution

I believe the first part would simply be e^{-(1/5000*10000)}=.1353

The second part I am at a loss on how to solve it.

 

[haruspex]

Can you construct the logical inverse of 'at least one still working'?