### Nines and Tens

Explain why it is that when you throw two dice you are more likely to get a score of 9 than of 10. What about the case of 3 dice? Is a score of 9 more likely then a score of 10 with 3 dice?

### Master Minding

Your partner chooses two beads and places them side by side behind a screen. What is the minimum number of guesses you would need to be sure of guessing the two beads and their positions?

### Odds and Evens

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

# At Least One...

##### Stage: 3 Challenge Level:

Imagine flipping a coin three times.
What's the probability you will get a head on at least one of the flips?

Charlie drew a tree diagram to help him to work it out:

He put a tick by all the outcomes that included at least one head.
How could Charlie use his tree diagram to work out the probability of getting at least one head?
How could he use it to work out the probability of getting no heads?
What do you notice about these two probabilities?

Devise a quick way of working out the probability of getting at least one head when you flip a coin 4, 5, 6... times.
What is the probability of getting at least one head when you flip a coin ten times?

************************

Once you've worked out a neat strategy for the coins problem, take a look at these related questions which can be solved in a similar way:

Imagine choosing a ball from this bag and then replacing it.

If you did this three times, what's the probability that you would pick at least one green ball?

What if you didn't replace the ball each time?

Imagine a class with 15 girls and 13 boys.
Three children are chosen at random to represent the class at School Council
What is the probability that there will be at least one boy?

Why not try the problem Same Number! next?