Combining probabilities

problem
Do you brush your teeth every day?

Age

14 to 18

Challenge level

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

Age

16 to 18

Challenge level

Can you devise a fair scoring system when dice land edge-up or corner-up?
problem
At least one...

Age

11 to 14

Challenge level

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?
problem
Same number!

Age

14 to 16

Challenge level

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

Age

14 to 18

Challenge level

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

Age

14 to 18

Challenge level

Explore the distribution of molecular masses for various hydrocarbons
problem
Taking chances

Age

11 to 14

Challenge level

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.
problem
The better choice

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

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?
problem
Voting paradox

Age

14 to 18

Challenge level

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?