Mia has knitted 3 left-hand gloves: 1 blue, 1 green, and 1 red - OCR - GCSE Maths - Question 9 - 2020 - Paper 3

To determine if Mia is correct, we first need to calculate the total number of pair combinations possible.

Mia has:

• Left-hand gloves: Blue (1), Green (1), Red (1)
• Right-hand gloves: Green (1), Red (1)

Calculating the total combinations:

• Pair (Blue, Green)
• Pair (Blue, Red)
• Pair (Green, Green)
• Pair (Green, Red)
• Pair (Red, Green)
• Pair (Red, Red)

Thus, the total combinations of left-hand and right-hand gloves are 5. Now, we will find the number of same-colour pairs available:

1. Green Pair (1 Green left + 1 Green right) = 1 combination
2. Red Pair (1 Red left + 1 Red right) = 1 combination

Total same colour pairs = 2.

Therefore, the probability of choosing a pair of the same color is:

$P(same \: color) = \frac{\text{Number of same color pairs}}{\text{Total pairs}} = \frac{2}{5}$

Thus, Mia's assertion of the probability being $\frac{2}{3}$ is incorrect.

Mia is incorrect because the probability should be $\frac{2}{5}$ and not $\frac{2}{3}$.