Reuben is playing a matching game with these cards - OCR - GCSE Maths - Question 11 - 2017 - Paper 1

To find the probability that Reuben wins the game, we determine the scenarios in which he picks different cards:

1. First Card Circle & Second Card Square

   • Probability: ( \frac{4}{9} \times \frac{5}{8} = \frac{20}{72} = \frac{5}{18} )

2. First Card Square & Second Card Circle

   • Probability: ( \frac{5}{9} \times \frac{4}{8} = \frac{20}{72} = \frac{5}{18} )

Now, we add these probabilities together:

$P(Win) = P(Circle, Square) + P(Square, Circle) = \frac{5}{18} + \frac{5}{18} = \frac{10}{18} = \frac{5}{9}$

Thus, the probability that Reuben wins the game is ( \frac{5}{9} ).