Question $2/$Vraag $2$

At a large construction site there are, on average, $9$ cement

mixer failures per month, which require an expensive re$-$

placement. Assume there are $30$ days in a month.

$($a$)$ What is the probability that the first concrete mixer

failure in a month only occurs after $16$ days?

$($b$)$ What is the probability that there are at most $5$ con$-$

crete mixer failures in a specific month?

$($c$)$ With each concrete mixer failure there is a $6\%$

probability that there will not be another concrete

mixer readily available for immediate replacement.

What is the probability that one or more concrete

mixers will not be immediately replaced in an av$-$

erage month?

$($d$)$ An automatic brick loader machine has a $0\mathrm{.}5\%$

probability of cracking a brick, and a customer will

complain if more than $1$ bricks per palette of $100$

is cracked. Assume that each brick loaded is an

independent event. What is the probability that a

palette of $100$ bricks results in a complaint?