This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — Here is the solution in the requested form for part a) i. (All three balls have the same colour): Step 1: Calculate the individual combination values. The combination formula is nk = (n!)/(k!(n-k)!). 53 = (5 × 4 × 3)/(3 × 2 × 1) = 10 43 = (4 × 3 × 2)/(3 × 2 × 1) = 4 33 = (3 × 2 × 1)/(3 × 2 × 1) = 1 123 = (12 × 11 × 10)/(3 × 2 × 1) = 220 Step 2: Substitute the calculated values into the expression. P(all three same colour) = (5)/(3) + 43 + 33123 P(all three same colour) = (10 + 4 + 1)/(220) Step 3: Simplify the expression to find the probability. P(all three same colour) = (15)/(220) P(all three same colour) = (3)/(44) The probability that all three balls have the same colour is (3)/(44). Send me the next one 📸