Fair or Not?

📌 CONCEPT: The probability of getting at least two heads when three fair coins are tossed is a measure of the number of successful outcomes divided by the total number of possible outcomes.

📐 RULE / FORMULA: The probability of at least two heads can be calculated using the binomial distribution formula, P(at least 2 heads) = P(2 heads) + P(3 heads).

💡 WORKED EXAMPLE: Let's consider the possible outcomes when tossing three coins: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT. Out of these 8 outcomes, 3 show 2 or 3 heads. So, P(at least 2 heads) = 3/8.

⚠️ COMMON MISTAKE: Students often make the mistake of considering only the number of combinations with exactly two heads and ignoring the combinations with three heads, which is incorrect because both cases contribute to the probability of getting at least two heads.