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
Note: For the product of two quantities to result in a fixed value, to find the minimum possible value for one of the quantities, maximize the other.
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.
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