Example #1b: Two Events: Conditioning

Part b) demonstrates how to calculate conditional probabilities. If A is an event and B is another event, then P(B|A) is the probability of B occurring given that A has already occurred. Also, P(B|A) is not generally equal to P(A|B).

The following formula is used to compute the conditional probability of B given A:

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

The computation of P(A and B) is discussed more fully in Example 5.1c.

As an example, suppose a marble is selected and it is only known that the marble is odd numbered. What is the probability the marble is Red given the marble is Odd?

P(Red|Odd) =P(Red and Odd) / P(Odd)
=(4/20) / (10/20)
=4/10

Conditional probabilities simplify in the following situations:

  1. If A and B are disjoint events, then P(B|A) = 0.
  2. If A and B are independent events, then P(B|A) = P(B).


Use the applet to compute other conditional probabilities. What is the probability of Red given Even? What is the probability of Blue given Even?

Part a): Basic Probability

Part c): And Law

Part d) Or Law

Example #1