DNA traces left at the scene of a crime can provide evidence in a trial. What does the DNA evidence actually prove? 

The giant squid has been the subject of myth for thousands of years, yet almost nothing was known about it as the only evidence of its existence was from dead specimens washed up on the shore or fragments found in the stomachs of sperm whales. The first observation of live animals did not occur until the beginning of the $21st$century.

Was it necessary to see a live animal in order to prove its existence?

The possibility of climate change is a major threat to the human race. Many people believe that climate change is caused by humans; however, providing conclusive evidence that can persuade all scientists and politicians alike has proven difficult, and so the issue remains controversial.

Why might scientists and politicians be persuaded by different forms of evidence? 

Imagine that you work for Company $A$. Try to present the data in such a way that emphasises that your company is the best.

Two rival companies publish their yearly sales revenue (in millions of US dollars). The figures for the previous years are shown in the table below.:

Now imagine that you work for Company$\mathrm{B}$. How might you change the presentation to show your company to be more successful? 

With a perfect die you should have an equal chance of rolling any of the numbers on its faces. A weighted die has an increased chance of rolling one of the numbers (often a six).

If you take a die and roll it once, does this tell you anything about whether it is weighted or not?

With a perfect die you should have an equal chance of rolling any of the numbers on its faces. A weighted die has an increased chance of rolling one of the numbers (often a six).

If you now roll it six times, the chances that each roll will give you a different number are about 1.5%. Does this mean that the die is weighted? 

 With a perfect die, you should have an equal chance of rolling any of the numbers on its faces. A weighted die has an increased chance of rolling one of the numbers (often a  six). If you take a die and roll it once, does this tell you anything about whether it is weighted or not? If you now roll it six times, the chances that each roll will give you a different number are about 1.5%. Does this mean that the die is weighted?

If you then roll the die more times and record the results in a table, how many times would you need to roll the die before you had enough evidence to say whether the die is weighted?