A bag contains one £5 note, one £10 note, one £20 note and one £50 note. Amaan picks two of the notes at random without replacement. Work out the probability that he has picked at least £30.

This is a probability problem without replacement. First, let's find the total number of ways Amaan can pick two notes. There are 4 choices for the first note. After picking one, there are 3 choices left for the second note. Total number of ordered pairs (outcomes) = 4 × 3 = 12. Next, let's find the number of pairs where the sum is at least £30 (i.e., £30 or more). We can list them systematically: - (£5, £10) = £15 (No) - (£5, £20) = £25 (No) - (£5, £50) = £55 (Yes) - (£10, £5) = £15 (No) - (£10, £20) = £30 (Yes) - (£10, £50) = £60 (Yes) - (£20, £5) = £25 (No) - (£20, £10) = £30 (Yes) - (£20, £50) = £70 (Yes) - (£50, £5) = £55 (Yes) - (£50, £10) = £60 (Yes) - (£50, £20) = £70 (Yes) Counting the "Yes" outcomes, we have 8 favourable outcomes. The probability is the number of favourable outcomes divided by the total number of outcomes. P(sum ≥ £30) = 8 / 12 This fraction can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 4. P(sum ≥ £30) = 2 / 3.