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

Since the probability of selecting a purple counter is 0.2, the probability of selecting either a red or a blue counter is given by: $P(Red ext{ or } Blue) = 1 - P(Purple) = 1 - 0.2 = 0.8$

From the ratio of red to blue counters, the total ratio parts are 3 + 17 = 20. This means:

• The probability of selecting a red counter is given by: $P(Red) = \frac{3}{20}$
• The probability of selecting a blue counter is: $P(Blue) = \frac{17}{20}$ To find the probability that Sam takes a red counter, we need to consider the total probability of drawing a non-purple counter, which equals 0.8. Thus, the probability of drawing a red counter from a non-purple counter is: $P(Red | Non-Purple) = \frac{P(Red)}{P(Red) + P(Blue)} \\ = \frac{\frac{3}{20}}{\frac{3}{20} + \frac{17}{20}} = \frac{3}{20} \times \frac{20}{20} = \frac{3}{20}$ To get the overall probability of drawing a red counter: $P(Red) = P(Red | Non-Purple) \times P(Non-Purple) = \frac{3}{20} \times 0.8 = \frac{3 imes 0.8}{20} = \frac{2.4}{20} = 0.12$