Definition:Two events *E* and *F* are said to be independent
if

Example:

We draw two cards one at a time from a
shuffled deck of 52 cards.

Are the two following events independent?

**E**- The first card is a heart.
**F**- The second card is a queen.

From the definition of conditional probability,
we need to find *P*(*F*|*E*) by computing

and .

or we showed that equivalently, *E* and *F* are independent if
and only if:

Beware this multiplication rule is ONLY available if and only if the events ARE independent.

Example:

De Méré's problem is whether
or not it is more likely to get
at least one double six in 24 throws
of a pair of dice or to get at least one
six in 4 throws of a die?

Essential to this argument is the fact that each throw of a die is independent of the preceding one.

The easier probability to compute is the complementary one:

and the complementary event

- Independence of more than two events 10/20
- The Craps principle 10/16
- Example of computation for craps 10/19