Example Question - coin flips
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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%.
Calculating Probability of Coin Flips
To solve this problem, we need to calculate the probability of flipping a coin twice and getting heads on the first flip and tails on the second flip. The probability of getting heads on a single flip is 1/2, and the probability of getting tails on a single flip is also 1/2. Since these two events are independent (the outcome of the first flip does not affect the outcome of the second flip), we can find the combined probability by multiplying the probabilities of the two individual events. So, the probability of getting heads first and then tails is: (1/2) * (1/2) = 1/4. Now to express this as a percentage, we convert the fraction to a percentage by multiplying by 100: 1/4 * 100% = 25%. Therefore, the probability of getting heads and then tails when flipping a coin twice is 25%.
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