Probability - conditional probabilities
Instructions below

[Applet - Conditional probabilities]
 The grey six-by-six box represents the 36 possibilities when 2 fair six-sided dice are thrown. There are 2 drop-down lists at the top of the screen. Make your choice using these lists. When you have chosen something in each list, you'll see that some of the squares in the six-by-six box are coloured red or yellow. We're going to investigate conditional probabilities using this screen. The coloured squares represent the number of combinations that satisfy condition B (the second condition from the right-hand list). Of these coloured squares, the red ones represent the combinations which also satisfy the first condition (A). There are two methods for calculating P(A|B) - "the probability that A occurs given that B is true". One involves counting coloured squares, the other uses a formula. You should investigate them both, to see how they relate to one another. If you press "Reverse", you swap the statements A and B. You should quickly see that P(A|B) is not, in general, equal to P(B|A). Play around and you should begin to understand what can be a tricky topic. Have fun!