Why Do We Multiply the Probabilities of Independent Events?

Date: 10/15/2009 at 22:05:25
From: Hannah
Subject: Why use multiplication to find the probability of two events

I would like to know the reasoning behind this topic.

P(A and B)= P(A)x P(B)

Why do we have to multiply the two probabilities, why can't we add
them together?  Thank you very much.

Date: 10/15/2009 at 23:38:02
From: Doctor Peterson
Subject: Re: Why use multiplication to find the probability of two events

Hi, Hannah.

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.

Does that help?

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/