# How likely? - November 2010, Stage 3&4

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...

##### Age 11 to 14 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?

##### Age 11 to 14 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?

### Sociable Cards

##### Age 11 to 14 Challenge Level:

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

### What Does Random Look Like?

##### Age 11 to 14 Challenge Level:

Engage in a little mathematical detective work to see if you can spot the fakes.

### Mathsland National Lottery

##### Age 14 to 16 Challenge Level:

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

### Last One Standing

##### Age 14 to 16 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?

### Same Number!

##### Age 14 to 16 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

##### Age 14 to 18 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.