For independent events, the probability of

bothoccurring is theproductof the probabilities of the individual events:Pr(AandB)=Pr(A∩B)=Pr(A)×Pr(B).

Example: if you flip a coin twice, the probability of heads both times is: 1/2×1/2=1/4.

I don’t understand why we multiply. I mean, I’ve memorized the operation by now, that we multiply for independent events; but

why, I don’t get it.If I have 4 bags with 3 balls, then I have 3×4=12 balls: This I understand. Multiplication is (the act of)

scaling.But what does scaling have to do with independent events? I don’t understand why we scale one event by the other to calculate Pr(A∩B), if A, B are independent.

Explain it to me as if I’m really dense, because I am. Thanks.

**Answer**

I like this answer taken from http://mathforum.org/library/drmath/view/74065.html :

”

It may be clearer to you if you think of probability as the fraction

of the time that something will happen. If event A happens 1/2 of the

time, and event B happens 1/3 of the time, and events A and B are

independent, then event B will happen 1/3 of the times that event A

happens, right? And to find 1/3 of 1/2, we multiply. The probability

that events A and B both happen is 1/6.

Note also that adding two probabilities will give a larger number than

either of them; but the probability that two events BOTH happen can’t

be greater than either of the individual events. So it would make no

sense to add probabilities in this situation.

“

**Attribution***Source : Link , Question Author : Emi Matro , Answer Author : blue-sky*