Probability
problem
Two and One
Terry and Ali are playing a game with three balls. Is it fair that
Terry wins when the middle ball is red?
problem
The Twelve Pointed Star Game
Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?
problem
You Never Get a Six
Charlie thinks that a six comes up less often than the other
numbers on the dice. Have a look at the results of the test his
class did to see if he was right.
problem
FA Cup
In four years 2001 to 2004 Arsenal have been drawn against Chelsea
in the FA cup and have beaten Chelsea every time. What was the
probability of this? Lots of fractions in the calculations!
problem
Limiting Probabilities
Given probabilities of taking paths in a graph from each node, use
matrix multiplication to find the probability of going from one
vertex to another in 2 stages, or 3, or 4 or even 100.
problem
Tricky Track
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first?
problem
Put Out
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
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?
problem
How Many Balls?
A bag contains red and blue balls. You are told the probabilities
of drawing certain combinations of balls. Find how many red and how
many blue balls there are in the bag.