There are only red counters, blue counters and purple counters in a bag - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 1

Let the number of purple counters be y. The total number of counters can be expressed as:

$ext{Total} = 3x + 17x + y = 20x + y$.

The probability of selecting a red counter is given by the ratio of the number of red counters to the total number of counters:

$P( ext{red}) = \frac{3x}{20x + y}$.

We know that the probability of selecting a purple counter is 0.2, which means:

$P( ext{purple}) = \frac{y}{20x + y} = 0.2$.

From this, we can express y in terms of x:

$y = 0.2(20x + y) \implies y = 4x + 0.2y \implies 0.8y = 4x \implies y = \frac{5x}{1}$.

Now, substituting y back into the probability of selecting a red counter:

$P( ext{red}) = \frac{3x}{20x + 5x} = \frac{3x}{25x} = \frac{3}{25}$.