Suppose that a flood light burns out during any one$-$hour period with probability

p $=0\mathrm{.}02.$ To complete an investigation, a group of detectives need the flood light to remain

illuminated without burning out for $10$ hours.

$($a$)$ At which hour is the flood light expected to burn out for the first time?

$($b$)$ What is the probability that the flood light burns out for the first time during the

tenth hour?

$($c$)$ What is the probability that the flood light will remain illuminated long enough for

the detectives to complete the investigatio