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