    Next: Independence of more than Up: Conditional Probability Previous: Monty Hall 10/14

## Independence 10/14 and 10/16

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      Next: Independence of more than Up: Conditional Probability Previous: Monty Hall 10/14
Susan Holmes
1998-12-07