Dependent Events

Dependent Events

If the occurrence of one event does affect the probability of the other occurring, then the events are dependent.

Conditional Probability

The probability of event B occurring that event A has already occurred is read "the probability of B given A" and is written: P(B|A)

General Multiplication Rule

Always works.

   P(A and B) = P(A) * P(B|A)

Example 4:

P(A) = 0.20, P(B) = 0.70, P(B|A) = 0.40
A good way to think of P(B|A) is that 40% of A is B. 40% of the 20% which was in event A is 8%, thus the intersection is 0.08.

	B	B'	Marginal
A	0.08	0.12	0.20
A'	0.62	0.18	0.80
Marginal	0.70	0.30	1.00

Independence Revisited

The following four statements are equivalent

1. A and B are independent events
2. P(A and B) = P(A) * P(B)
3. P(A|B) = P(A)
4. P(B|A) = P(B)

The last two are because if two events are independent, the occurrence of one doesn't change the probability of the occurrence of the other. This means that the probability of B occurring, whether A has happened or not, is simply the probability of B occurring.