Challenge Level

In the Mathsland National Lottery, six balls painted with the numbers 1 to 6 are placed in a bag.

To enter, you choose three numbers.

To win, your numbers must match (in any order) the three numbers that are drawn from the bag.

**What is the probability of winning?**

The Mathsland Lottery organisers decide to change to a simpler system where you just choose two numbers from the six, and then two numbers are drawn from the bag.

To win, both of your numbers must match.

**How will this affect your chance of winning?**

The two-number lottery is very unpopular, so the organisers move to a four-number (six ball) lottery instead.

**How will this affect your chance of winning?**

In their effort to find the most popular lottery, the organisers also trial a one-number and a five-number (six ball) lottery.

**What can you say about the chances of winning these?**

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The Mathsland Lottery organisers decide to move to a 10-ball lottery, but they can't decide how many numbers should be drawn.

The organisers want to make the chance of winning as low as possible! Can you advise them?

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When the UK National Lottery was first introduced it allowed you to choose six numbers from 49. What is the probability of winning the jackpot in the UK lottery?