# Flipping a coin - heads or galley - 1

Traditionally, we say that a coin has two sides, 'heads' and 'tails', although sometimes there might be other things on each side of a coin. For example, in the picture, you can see a Roman Denarius made around 113 BC. It has the double head of the Roman God Janus on one side and an oared galley on the other one! The coin has two sides so if you flipped the coin into the air and watched it land, half the time you might expect to see a 'head' and half the time you might expect to see a 'galley'.

**Q1.** If you flipped the coin ten times, would you expect to see the coin land exactly 5 times on the head and 5 times on the galley? Why / Why not?**Q2.** Explain your answer to Q1.**Q3.** If you flipped the coin ten thousand times, how many times would you expect to see a head and how many times would you expect to see a galley?**Q4.** Explain your answer to Q3.

If you flipped the coin ten thousand times, you might expect to see a graph that looks something like this:

If you flipped the coin ten thousand times again, you might see a graph similar to the above one or you might see a graph something like this:

**Q5.** If you had a few weeks to spare and repeated the experiment to flip the coin 10 000 times fifty times, and the results kept looking like FIG 1 above, what might that tell you?

The thought of us sitting there flipping coins hundreds of thousands of times, recording results and drawing graphs for a few weeks is not a nice one! What we need to do is to model this problem. We need to write a program that will flip the coin for us as many times as we want and show us the results.