### Rain or Shine

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.

### Squash

If the score is 8-8 do I have more chance of winning if the winner is the first to reach 9 points or the first to reach 10 points?

### Card Game (a Simple Version of Clock Patience)

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in one pile. What is the probability that you win?

# Which Spinners?

##### Age 14 to 18 Challenge Level:

In the interactivity below there are two spinners.
When you press "One spin", the computer spins them once and adds (or finds the difference between) the numbers.

You can also spin 100 or 1000 times at once. The interactivity records the results in the relative frequency chart.
Warning - the computer needs a little bit of thinking time to do 1000 spins!

Experiment with different pairs of spinners.

What features do you notice on the bar charts that you produce?

Can you come up with ways of predicting what a chart will look like before you produce it?

### The challenge

The bar charts below were generated on the interactivity using different combinations of spinners.

Can you deduce which spinners were used to create each bar chart?

Can you explain how you used the information provided by the bar charts to work it out?

(You can download all eight bar charts here, or click on each chart to see a bigger version)

 A B C D E F G H

Final challenge

Imagine you had 1-20 and 1-30 spinners. Describe in as much detail as you can what the relative frequency bar charts would look like for:

• The sum of two 1-30 spinners
• The difference between two 1-20 spinners
• The sum of a 1-20 and a 1-30 spinner
• The difference between a 1-20 and a 1-30 spinner

Try to provide a good explanation to convince us that your descriptions of the bar charts are correct.

This resource is part of the collection Statistics - Maths of Real Life