A bag contains 25 discs. 11 are red, 9 are blue and 5 are yellow. Ashley picks three of the discs at random without replacement. Ashley's first disc is red. Work out the probability that all three discs are different colours.

This is a conditional probability problem because we are given information about the first event: "Ashley's first disc is red." Step 1: Update the contents of the bag. Originally: 11R, 9B, 5Y (Total 25) After one red is picked: 10R, 9B, 5Y (Total 24) Step 2: Determine the required outcomes for the next two picks. For all three discs to be different colours, and knowing the first is red, the next two must be one blue and one yellow. There are two possible orders for this to happen: - Order 1: Second is Blue, Third is Yellow (B, Y) - Order 2: Second is Yellow, Third is Blue (Y, B) Step 3: Calculate the probability of each order. - P(Order 1: B, Y) = P(2nd is Blue) × P(3rd is Yellow, given 2nd was Blue) = (9/24) × (5/23) (After picking a blue, 5 yellow are left out of 23) = 45/552 - P(Order 2: Y, B) = P(2nd is Yellow) × P(3rd is Blue, given 2nd was Yellow) = (5/24) × (9/23) (After picking a yellow, 9 blue are left out of 23) = 45/552 Step 4: Add the probabilities of the two possible orders. Since either order satisfies the condition, we add their probabilities: Total Probability = P(B, Y) + P(Y, B) = 45/552 + 45/552 = 90/552. Step 5: Simplify the fraction. Both 90 and 552 are divisible by 6. 90 ÷ 6 = 15 552 ÷ 6 = 92 So the probability is 15/92.