Florin Frenti operates a small, used car lot that has three Mercedes (M1, M2, M3) and two Toyotas (T1, T2). Two customers, Cezara and Anda, come to his lot, and each selects a car. The customers do not know each other, and there is no communication between them. Let the events A and B be defined as follows:
A: The customers select at least one Toyota.
B: The customers select two cars of the same model.
a. Identify all pairs of cars in the sample space.
b. Define event A.
c. Define event B.
d. Define the complement of A.
e. Show that (A ∩ B) ( (A ∩ B) = B.
f. Show that A ( (A ∩ B) = A ( B.