Study guides › Level 6 · Master

The chance of two things both happening

Level 6 · Master · for questions like “You flip a coin and roll a number cube. What is the chance of heads and an even number?”

💡 The idea

When two things don't affect each other, multiply their chances.

🪜 The steps

1. Find the first chance (heads: 1/2).
2. Find the second chance (an even number: 3 of 6 = 1/2).
3. Multiply: 1/2 × 1/2 = 1/4.

✏️ Worked examples

1. Heads and an even number: 1/2 × 3/6 = 1/2 × 1/2 = 1/4.

2. Tails and a number bigger than 4: 1/2 × 2/6 = 1/2 × 1/3 = 1/6.

⚠️ Watch out

• “And” means multiply. Adding gives the wrong answer.
• Count carefully on the cube: “bigger than 4” is 5 and 6, which is 2 numbers.

🎯 Try these

1. Heads and a 6
2. Tails and an odd number
3. Heads and a number less than 3

Answers: 1) 1/12 2) 1/4 3) 1/6

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.