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