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Let's break down and solve the problem step by step:

1. **Lewis's goal** is to raise £100 for charity.
2. **The competition's details**:
   - The probability of winning is \( \frac{1}{60} \).
   - The prize for winning is £10.
3. **There are 1200 entrants**, and we need to determine the minimum charge per person that will ensure Lewis raises his target of £100, despite having to pay out prizes to winners.

### Step 1: Calculate expected number of winners
Since 1200 people enter and the probability of winning is \( \frac{1}{60} \), the expected number of winners is:
\[
\text{Expected winners} = 1200 \times \frac{1}{60} = 20
\]
So, on average, there will be 20 winners.

### Step 2: Calculate the total prize payout
Each winner gets £10, so the total payout for 20 winners is:
\[
\text{Total payout} = 20 \times 10 = £200
\]

### Step 3: Total amount Lewis needs to raise
To hit his target, Lewis needs to raise £100 for charity, but he also needs to cover the £200 in prize payouts. Therefore, the total amount he needs to raise from the entrants is:
\[
\text{Total amount needed} = £100 + £200 = £300
\]

### Step 4: Calculate the minimum charge per person
There are 1200 people entering, so the minimum amount he needs to charge each person is:
\[
\text{Charge per person} = \frac{£300}{1200} = £0.25
\]
Since the answer must be in pence:
\[
\text{Charge per person in pence} = 0.25 \times 100 = 25 \text{ pence}
\]

### Final Answer:
The minimum charge per person should be **25 pence**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the charge change if the prize were £15 instead of £10?
2. What if the probability of winning were \( \frac{1}{100} \)? How would this affect the charge?
3. How much would each person need to pay if there were only 1000 entrants instead of 1200?
4. What if Lewis wanted to raise £200 instead of £100 for charity? How would this change the charge per person?
5. How does the expected number of winners affect the overall pricing strategy in a competition like this?

**Tip**: Understanding how probability affects expected outcomes is crucial in scenarios like this. You can apply this concept to many areas involving uncertainty and risk!

Lewis wants to raise £100 for charity. He organizes a competition in which the probability of winning is 1/60 and the winning prize is £10. If 1200 people pay to enter, what is the minimum he should charge each person so that he can expect to hit his target? Give your answer in pence.

Learn how to calculate the minimum entry fee required to raise £100 for charity in a competition with a 1/60 probability of winning and a prize of £10. Understand key concepts such as probability, expected value, and algebraic formulas. Suitable for Grades 9-12 students.

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