# How likely? - November 2010, Stage 4&5

In this month's problems we invite you to experiment with a range of situations whose outcomes may surprise you. Can you use mathematics to explain why you shouldn't be so surprised?

## Problems

### At Least One...

##### Stage: 3 and 4 Challenge Level:

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?

### Do You Feel Lucky?

##### Stage: 3 and 4 Challenge Level:

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

### Last One Standing

##### Stage: 3 and 4 Challenge Level:

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

### Mathsland National Lottery

##### Stage: 4 Challenge Level:

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

### Same Number!

##### Stage: 4 Challenge Level:

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

### Weekly Challenges

##### Stage: 4 and 5 Challenge Level:

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

### Interactive Workout - Mathmo

##### Stage: 5 Short Challenge Level:

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

### Discussing Risk and Reward

##### Stage: 5 Challenge Level:

10 starting points for risk vs reward

### Dicey Dice

##### Stage: 5 Challenge Level:

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

### X-dice

##### Stage: 5 Challenge Level:

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

### The Derren Brown Coin Flipping Scam

##### Stage: 5 Challenge Level:

Calculate probabilities associated with the Derren Brown coin scam in which he flipped 10 heads in a row.