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
Step 1: Calculate the percentages for each category using the given information. Let F be Football, H be Hockey, and B be Basketball. Given: P(F) = 0.60 P(H) = 0.45 P(B) = 0.40 P(F H) = 0.30 P(F B) = 0.20 P(H B) = 0.15 P(F H B) = 0.10 First, calculate the percentages of playing exactly two games: P(F and H only) = P(F H) - P(F H B) = 0.30 - 0.10 = 0.20 P(F and B only) = P(F B) - P(F H B) = 0.20 - 0.10 = 0.10 P(H and B only) = P(H B) - P(F H B) = 0.15 - 0.10 = 0.05 Next, calculate the percentages of playing exactly one game: P(F only) = P(F) - (P(F and H only) + P(F and B only) + P(F H B)) P(F only) = 0.60 - (0.20 + 0.10 + 0.10) = 0.60 - 0.40 = 0.20 $P(H only) = P(H) - (P(F and H only) + P(H and B only