This is the question that I have, so I solved the first two parts very easily. The first part (i)
Then the part (ii)
Now, I dont know how to do the final part of the question (it is too confusing) with 10 bulbs switching on simultaneously and probability must be atleast 0.9, can someone solve this for me with a short brief explanation to each step
The idea is to simply calculate the probability that a given lightbulb is still on by time $t$. Then since the lifetime of each lightbulb in the display is independent of the others, the probability that all 10 are still on at time $t$ is given by the single-bulb probability raised to the $10^{\rm th}$ power. Then choose the largest $t$ such that this probability is at least $0.9$.