If two events X and Y are independent, then the probability that both occur (P X AND Y) = P(X) . P(Y) and it is given that P(X) . P(Y) = 0.45


Here we know that the probability of an event 'E' is limited to the range 0 < P(E) < 1
The maximum probability that an event may occur is 1 and since we are trying to establish a lower bound for P(X), maximize P(Y) i.e. P(Y) = 1.
Given this situation:
P(X) x 1 = 0.45 \( \implies \) P(X) = 0.45.
Thus P(X) can never fall below this value and thus Qty A is greater.