If a coin is tossed 5 times, what is the probability that it lands heads up at least once?

📌 CONCEPT: The probability of an event occurring is the number of favorable outcomes divided by the total number of possible outcomes.

📐 RULE / FORMULA: The probability of getting heads at least once in 5 tosses can be found using the principle of complementary probability, which states that P(event) = 1 - P(not event). In this case, the probability of getting heads at least once is 1 minus the probability of getting tails in all 5 tosses.

💡 WORKED EXAMPLE: Let's consider a scenario where we toss a coin 5 times. The sample space consists of all possible outcomes, which are HHHHH, HHHHT, HHHHT, ..., TTTTT. The probability of getting tails in all 5 tosses is (1/2)^5 = 1/32. Using the principle of complementary probability, the probability of getting heads at least once is 1 - 1/32 = 31/32.

⚠️ COMMON MISTAKE: Students often get confused between the probability of an event occurring and the probability of it not occurring. They might forget to use the principle of complementary probability and calculate the probability directly, which would be incorrect.