Tossing Two Biased Coins?

📌 CONCEPT: The probability of two events occurring together is the product of their individual probabilities, which is an essential concept in the study of probability involving more than one event.

📐 RULE / FORMULA: To find the probability of both events occurring together, we multiply the probabilities of the individual events. In this case, the probability of both coins landing on heads is given by P(A ∩ B) = P(A) × P(B).

💡 WORKED EXAMPLE: If the probability of the first biased coin landing on heads is 60% or 0.6 and the probability of the second biased coin landing on heads is 80% or 0.8, then the probability that they both land on heads is 0.6 × 0.8 = 0.48 or 48%. This can be calculated using the formula P(A ∩ B) = P(A) × P(B).

⚠️ COMMON MISTAKE: Students often mistakenly calculate the probability of both events occurring together by adding their individual probabilities, instead of multiplying them. For example, they might add 0.6 and 0.8 to get 1.4, which is incorrect.