$($a$)$ Construct a fault tree for a flat tire. A flat tire can occur as a result of either a mechanical failure or an operational mishap. Operational mishaps include hitting objects in the roadway and running into an off$-$road object such as a curb or the edge of a culvert. Mechanical failure can result from a combination of high tire pressure, high tire temperature, and excessive tire wear.

$($b$)$ Construct an event tree where the initiating event is a flat tire resulting from an operational failure. Event tree should include $4$ or $5$ branches