Combining probabilities

How can we find out answers to questions like this if people often lie?

Can you devise a fair scoring system when dice land edge-up or corner-up?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Investigate the molecular masses in this sequence of molecules and deduce which molecule has been analysed in the mass spectrometer.

Explore the distribution of molecular masses for various hydrocarbons

This article, for students and teachers, is mainly about probability, the mathematical way of looking at random chance and is a shorter version of Taking Chances Extended.

Here are two games you can play. Which offers the better chance of winning?

After transferring balls back and forth between two bags the probability of selecting a green ball from bag 2 is 3/5. How many green balls were in bag 2 at the outset?

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?