Example Question - at least twice

Probability of Landing Heads at Least Twice in Three Coin Flips

The image shows a probability tree diagram for flipping a coin three times. To find the probability of landing on heads at least twice, you must consider all the possible outcomes that include two or three heads. The tree diagram shows the following outcomes with at least two heads: 1. Heads → Heads → Heads (HHH) 2. Heads → Heads → Tails (HHT) 3. Heads → Tails → Heads (HTH) 4. Tails → Heads → Heads (THH) Since each flip of a fair coin has two possible outcomes (heads or tails) and the flips are independent, each branch in this tree has a probability of 1/2. Now we can calculate the probabilities for each of the four desired outcomes: 1. P(HHH) = 1/2 * 1/2 * 1/2 = 1/8 2. P(HHT) = 1/2 * 1/2 * 1/2 = 1/8 3. P(HTH) = 1/2 * 1/2 * 1/2 = 1/8 4. P(THH) = 1/2 * 1/2 * 1/2 = 1/8 Now add these probabilities up to get the total probability of getting at least two heads in three tosses: P(at least two heads) = P(HHH) + P(HHT) + P(HTH) + P(THH) = 1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2 So, the probability of landing on heads at least twice in three flips of a coin is 1/2 or 50%.