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Conditional Probability

The conditional probability that an event A happens if B is true (or has happened already) is denoted by P(A|B). In the homework you will analyze a few problems in which conditional probability plays a role. On this page you can test your own understanding of the concept in a simpler example.

The interactive table below lists, on the extreme left, the possible total values of the number of dots you see on the top faces of two dice. In the table itself you can fill in the probability that at least one of the two dice shows a 4 (for instance), given that the total of the throw of the two dice is fixed at the indicated number.

For instance, if you look at the box on the sixth row (corresponding to a sum of 7) in the fourth column (corresponding to at least one die showing a 4), then you should fill in here the probability

P(at least one of the two dice shows a 4| the sum of the two dice is 7).
Since there are 6 different combinations (1-6 ; 2-5; 3-4; 4-3; 5-2; 6-1) that add up to 7, and two of these show a 4, the probability is 2/6 = 1/3 . If you fill in 1/3, then a letter C will appear, showing your answer is Correct; an incorrect answer is indicated by an I (for Incorrect).

Whenever your entry is smaller than 1 and bigger than 0, please enter it as the simplest fraction - for instance, you should enter 1/2 rather than 0.5 or .5 or 2/4 or 3/6 etc.

Try this for yourself, until you feel confident that you completely understand the concept of conditional probability.

Practice
Conditional Probabilities