$.$ State the sample space for the following experiments:

$($a$)$ You are an engineer working for DoC and are responsible for annually inspecting bridges. You check

two bridges, that can either pass $($P$)$ or fail $($F$).$ The sample space is the set of possible sequences

of outcomes from checking the two bridges.

$($b$)$ Drawing $4$ bolts from a bucket containing both coach and hex bolts and counting the number of

hex bolts you get.

$($c$)$ Counting the number of widgets you need to check to observe the first one with a defect.