If there are 2 independent event A and B, we find the probability of their intersection as product of their respective probability. Though I know how it is deduced but I don't seem to find proper intuition behind it. I don't expect any derivation. Kindly someone help.
2026-04-06 09:47:47.1775468867
How multiplying probabilities works?
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A and B being independent means that whether A happens or not does not alter the probability of B occurring or not. So, when A and B are independent, we basically we have that $P(A|B) = P(A)$ (this disregards the case where $P(B)=0$, but for convenience sake let's assume $P(B) >0$).
Now, in general we say that the probability for the intersection of A and B to happen is to have one happen multiplied by the other the happen as well given that the first one happens (so basically: $P(A \cap B) = P(A) * P(B|A)$ . But we just saw that when they are independent, then $P(B|A) = P(B)$, and so $P(A \cap B) = P(A) * P(B)$