Conditional probability

problem
Dicey dice

Age

16 to 18

Challenge level

Invent a set of three dice where each one is better than one of the others?
problem
Drug testing

Age

16 to 18

Challenge level

How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?
problem
Rain or shine

Age

16 to 18

Challenge level

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
problem
X-dice

Age

16 to 18

Challenge level

Explore these X-dice with numbers other than 1 to 6 on their faces. Which one is best?
problem
Ante up

Age

16 to 18

Challenge level

Use cunning to work out a strategy to win this game.
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?