To determine the probability of flipping tails 4 times in a row with a fair coin, we need to consider the likelihood of getting tails on each individual flip. A fair coin has two sides: heads and tails. Therefore, the probability of getting tails on a single flip is 1/2.
When calculating the probability of multiple independent events occurring in sequence, we multiply the probabilities of each event. Since the flips are independent, the probability of getting tails four times in a row can be calculated as follows:
P(Tails 4 times) = P(Tails) × P(Tails) × P(Tails) × P(Tails) = (1/2) × (1/2) × (1/2) × (1/2)
This simplifies to:
P(Tails 4 times) = (1/2)⁴ = 1/16
Thus, the probability of flipping tails four times in a row is 1/16, which is equivalent to 0.0625 or 6.25%. This means that if you were to flip a coin four times, you would expect to get all tails only once in every sixteen attempts, on average.