# Year 10+ Puzzles

### Chapters

### Solution: Coloured Cards Puzzle

# Solution: Coloured Cards Puzzle

## The Puzzle:

Three cards are placed in a hat. They are

- A card that is coloured red on both sides.
- A card that is coloured green on both sides.
- A card that is coloured green on one side and red on the other side.

## The Solution:

It's very tempting to say that the probability is \(\dfrac{1}{2}\), but this is incorrect. This is actually a conditional probability problem: we're looking for the probability that the card that has been drawn is the card that is green
on both faces,
**given** that the first face is green. Using the formula for conditional probability, this is \(\dfrac{1 \times \dfrac{1}{3}}{\dfrac{1}{2}} = \dfrac{2}{3}\).

I have to admit, this still makes my brain hurt. Let's try an intuitive explanation. Once the card is drawn from the hat and placed face upwards, we know that it is not the card that is coloured red on both sides. So, there are three possibilities for the second face of the card that has been drawn:

- It is the bottom face of the card that is green on both sides.
- It is the top face of the card that is green on both sides.
- It is the red face of the card that is red on one side and green on the other.

In two of these three cases, the other side of the card will be green, so the probability that the second face is green is \(\dfrac{2}{3}\).

### Description

This series of puzzles are for Year 10 or higher students, these puzzles tests your skills and also train you with problem solving and thinking out of the box

### Audience

Year 10 students or higher

### Learning Objectives

Solving puzzles

Author: Subject Coach

Added on: 28th Sep 2018

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