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# At Least One...

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Age 11 to 14

Challenge Level

*At Least One... printable sheet*

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?

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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 (which contains six red balls and four blue balls) 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?