Mathematics
Mathematics
Problem
Three identical fair coins are tossed at the same time. (a) List all possible outcomes of the experiment using ordered triples of H (head) and T (tail). (b) Calculate the probability that at least two heads appear in the three tosses.Intuitive explanation
When you toss multiple coins, the key is recognizing that each coin's outcome is independent—what one does doesn't affect the others. By systematically listing all equally likely outcomes as ordered triples, you create a complete sample space. Then "at least two heads" means you count outcomes with exactly two heads or exactly three heads, which is much easier than using complements here. The ordered structure (like HHT vs HTH) matters because each distinct arrangement is a separate outcome.
Intuitive explanation
When you toss multiple coins, the key is recognizing that each coin's outcome is independent—what one does doesn't affect the others. By systematically listing all equally likely outcomes as ordered triples, you create a complete sample space. Then "at least two heads" means you count outcomes with exactly two heads or exactly three heads, which is much easier than using complements here. The ordered structure (like HHT vs HTH) matters because each distinct arrangement is a separate outcome.