This asks for the probability that the particle stays more than 3 seconds, given that it does not stay longer than 4 seconds, so 4 or less. From the definition: The event R3 ∩ Rc 4 describes: longer...

This asks for the probability that the particle stays more than 3 seconds, given that it does not stay longer than 4 seconds, so 4 or less. From the definition:

The event R3 ∩ Rc 4 describes: longer than 3 but not longer than 4 seconds. Furthermore, R3 is the disjoint union of the events R₃∩Rc
₄
and R3∩R₄
= R₄