In particular, the formula for the efficiency of Aloha should look like
(TRF)/(TRF + CT)Where CT is the time stations spend in contention before one station wins and gets its packet delivered.
Given our experience deriving formulas for expected values, it is clear that the correct for CT will involve the probability, p, that a given attempt to transmit a packet fails due to a collision. The bigger this probability, the bigger CT will be.
Basically, any two stations that get the urge to transmit within 2 TRF of one another will collide.
Accordingly, stations in slotted Aloha collide only if the become ready to transmit within TRF of one another. Stations in pure Aloha collide if they become ready to transmit within twice this time period.